Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
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1A sphere has radius $3$ cm. Work out the volume of the sphere. Give your answer in terms of $\pi$. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A$108\pi$ cm³B$12\pi$ cm³C$36\pi$ cm³D$9\pi$ cm³
2A pyramid has a square base of side $5$ cm. The apex is directly above the centre of the base and the perpendicular height of the pyramid is $6$ cm. Work out the volume of the pyramid. Give your answer in cm³.
A100B150C31D50
3A cone has base radius $8$ cm and vertical height $15$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A12.7B17C23D16
4The diagram shows a solid square-based pyramid. The base is a square of side $6$ cm and each of the four triangular faces has a slant height of $8$ cm. Work out the total surface area of the pyramid.
A96B84C228D132
5A cone has base radius $4$ cm and vertical height $12$ cm. Work out the volume of the cone. Give your answer in terms of $\pi$.
6Two identical solid square-based pyramids each have a square base of side $3$ cm. Together they have a total volume of $54$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A9B27C18D3
7A solid hemisphere and a solid cylinder both have radius $12$ cm. The cylinder has height $10$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A12 : 11B9 : 5C6 : 11D9 : 11
8A solid cone has base radius $6$ cm and slant height $9$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A283B1130C396D170
9A solid hemisphere has radius $7$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A616B462C308D154
10A cylindrical tube has internal diameter $10$ cm and height $35$ cm. Balls of diameter $6$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A5B24C3D6
11A pyramid has a square base of side $9$ cm and a volume of $216$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A72B216C3D8
12A frustum is made by removing a small cone from the top of a larger cone, with the cut parallel to the base. The larger cone has base radius $16$ cm and vertical height $30$ cm. The small cone that is removed has base radius $8$ cm and vertical height $15$ cm. Work out the volume of the frustum. Give your answer in terms of $\pi$. (Volume of a cone $= \dfrac{1}{3}\pi r^2 h$.)
13A solid cone has base radius $4$ cm and vertical height $3$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$, where $l$ is the slant height.)
A62.8B101C88.0D113
14A solid cylinder has radius $3$ cm and height $5$ cm. A solid sphere has the same volume as the cylinder. Work out the radius of the sphere. Give your answer correct to 3 significant figures. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A3.23B5.13C3.56D5.81
15The net of a cone is a sector of a circle of radius $12$ cm with an angle of $180°$ at the centre. The net is folded to make a cone of slant height $12$ cm. Work out the vertical height of the cone.
A13.4B6C11.0D10.4
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3A cone has base radius $8$ cm and vertical height $15$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A17B23C12.7D16
4A pyramid has a square base of side $6$ cm. The apex is directly above the centre of the base and the perpendicular height of the pyramid is $5$ cm. Work out the volume of the pyramid. Give your answer in cm³.
A60B41C120D180
5A cone has a base radius of $10$ cm and a vertical height of $22$ cm. Work out the volume of the cone.
A9220B6910C2300D230
6A solid cone has base radius $3$ cm and slant height $7$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A226B123C94.2D66.0
7A hemisphere has a diameter of $16$ cm. Work out the volume of the hemisphere.
A2140B1070C8580D268
8A solid hemisphere has radius $11$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A760B1140C1520D380
9Two identical solid square-based pyramids each have a square base of side $6$ cm. Together they have a total volume of $240$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A10B60C20D3
10A solid hemisphere and a solid cylinder both have radius $3$ cm. The cylinder has height $3$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A1 : 1B1 : 2C3 : 4D3 : 2
11A pyramid has a square base of side $8$ cm and a volume of $384$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A18B144C6D384
12A sphere has a volume of $288\pi$ cm³. Work out the radius of the sphere. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A12B8C6D7
13A cone has slant height $8$ cm and base radius $r$ cm. The total surface area of the cone is $65\pi$ cm². Work out the value of $r$. (Total surface area of a cone $= \pi r^2 + \pi r l$.)
A10B5C8D6
14The diagram shows a frustum formed by removing a small cone from a larger cone. The larger cone has base radius $16$ cm and slant height $34$ cm. The frustum has a top radius of $8$ cm. Work out the total surface area of the frustum. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$, where $l$ is the slant height.)
A2090B2710C1280D2290
15A solid square-based pyramid has a base of side $9$ cm. A solid hemisphere has radius $3$ cm. The volume of the hemisphere is $50\%$ of the volume of the pyramid. Work out the perpendicular height of the pyramid. Give your answer correct to 3 significant figures. (Volume of a hemisphere $= \dfrac{2}{3}\pi r^3$.)
A1.40B8.38C2.09D4.19
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4A cone has base radius $5$ cm and vertical height $12$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A14.0B17C10.9D13
5A cone has base radius $10$ cm and slant height $19$ cm. Work out the curved surface area of the cone (the curved part only). Give your answer in terms of $\pi$. (Curved surface area of a cone $= \pi r l$.)
6A solid hemisphere has radius $6$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A113B339C452D226
7A pyramid has a square base of side $6$ cm and a volume of $60$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A60B5C30D2
8A sphere has a diameter of $12$ cm. Work out the volume of the sphere.
A151B905C452D7240
9A solid hemisphere and a solid cylinder both have radius $9$ cm. The cylinder has height $8$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A27 : 34B18 : 17C9 : 17D27 : 16
10A cylindrical tube has internal diameter $12$ cm and height $74$ cm. Balls of diameter $10$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A15B7C6D8
11A solid cone has base radius $6$ cm and slant height $15$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A283B509C1810D396
12A sphere has a volume of $36\pi$ cm³. Work out the radius of the sphere. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A5B6C4D3
13Two cones are joined base-to-base to make a solid. Both cones have base radius $r$ cm. One cone has slant height $4r$ cm and the other has slant height $5r$ cm. The total curved surface area of the solid is $300\pi$ cm². Work out the value of $r$. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A5.77B33.3C5.22D3.87
14The diagram shows a frustum formed by removing a small cone from a larger cone. The larger cone has base radius $24$ cm and slant height $51$ cm. The frustum has a top radius of $16$ cm. Work out the total surface area of the frustum. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$, where $l$ is the slant height.)
A3950B4750C6460D2140
15The net of a cone is a sector of a circle of radius $20$ cm with an angle of $144°$ at the centre. The net is folded to make a cone of slant height $20$ cm. Work out the vertical height of the cone.
A8B21.5C12D18.3
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2The diagram shows a solid square-based pyramid. The base is a square of side $8$ cm and each of the four triangular faces has a slant height of $10$ cm. Work out the total surface area of the pyramid.
A160B224C144D384
3A cone has base radius $6$ cm and slant height $10$ cm. Work out the curved surface area of the cone (the curved part only). Give your answer in terms of $\pi$. (Curved surface area of a cone $= \pi r l$.)
A$60\pi$ cm²B$120\pi$ cm²C$96\pi$ cm²D$36\pi$ cm²
4A sphere has radius $9$ cm. Work out the volume of the sphere. Give your answer in terms of $\pi$. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
5A cone has a base radius of $6$ cm and a vertical height of $16$ cm. Work out the volume of the cone.
A2410B603C1810D101
6A solid hemisphere and a solid cylinder both have radius $8$ cm. The cylinder has height $11$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A8 : 19B12 : 19C16 : 19D12 : 11
7A sphere has a diameter of $10$ cm. Work out the volume of the sphere.
A4190B524C105D262
8A solid hemisphere has radius $11$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A760B1520C380D1140
9A solid cone has base radius $9$ cm and slant height $14$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A396B3820C650D905
10A pyramid has a square base of side $12$ cm and a volume of $624$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A624B156C13D4
11A cylindrical tube has internal diameter $7$ cm and height $39$ cm. Balls of diameter $5$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A7B8C22D5
12VABCD is a pyramid with a square base ABCD of side $10$ cm. The apex V is directly above the centre X of the base. Each slant edge (such as VC) is $10$ cm. Work out the volume of the pyramid.
A0B333C236D707
13A frustum is made by removing a small cone from the top of a larger cone, with the cut parallel to the base. The larger cone has base radius $15$ cm and vertical height $36$ cm. The small cone that is removed has base radius $5$ cm and vertical height $12$ cm. Work out the volume of the frustum. Give your answer in terms of $\pi$. (Volume of a cone $= \dfrac{1}{3}\pi r^2 h$.)
14A solid cylinder has radius $5$ cm and height $8$ cm. A solid sphere has the same volume as the cylinder. Work out the radius of the sphere. Give your answer correct to 3 significant figures. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A5.85B8.43C5.31D12.2
15A sphere has a volume of $288\pi$ cm³. Work out the radius of the sphere. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A12B8C6D7
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3A cone has base radius $8$ cm and slant height $20$ cm. Work out the curved surface area of the cone (the curved part only). Give your answer in terms of $\pi$. (Curved surface area of a cone $= \pi r l$.)
4The diagram shows a solid square-based pyramid. The base is a square of side $10$ cm and each of the four triangular faces has a slant height of $15$ cm. Work out the total surface area of the pyramid.
A400B700C250D300
5A cone has base radius $7$ cm and vertical height $24$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A26.0B25C23.0D31
6A cylindrical tube has internal diameter $14$ cm and height $70$ cm. Balls of diameter $10$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A7B5C20D8
7A solid cone has base radius $11$ cm and slant height $16$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A6460B553C933D1310
8A sphere has a radius of $4$ cm. Work out the volume of the sphere.
A2140B67.0C134D268
9A pyramid has a square base of side $12$ cm and a volume of $240$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A5B60C2D240
10A solid hemisphere has radius $10$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A628B314C942D1260
11Two identical solid square-based pyramids each have a square base of side $3$ cm. Together they have a total volume of $42$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A14B21C2D7
12A cone has slant height $13$ cm and base radius $r$ cm. The total surface area of the cone is $114\pi$ cm². Work out the value of $r$. (Total surface area of a cone $= \pi r^2 + \pi r l$.)
A12B7C6D13
13VABCD is a pyramid with a square base ABCD of side $6$ cm. The apex V is directly above the centre X of the base. Each slant edge (such as VC) is $15$ cm. Work out the volume of the pyramid.
A165B173C180D518
14A sphere has a surface area of $400\pi$ cm². Work out the volume of the sphere. Give your answer correct to 3 significant figures. (Surface area $= 4\pi r^2$, volume $= \dfrac{4}{3}\pi r^3$.)
A2090B3140C4190D1260
15A sphere has a volume of $\dfrac{4000\pi}{3}$ cm³. Work out the radius of the sphere. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A11B20C12D10
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3A pyramid has a square base of side $9$ cm. The apex is directly above the centre of the base and the perpendicular height of the pyramid is $11$ cm. Work out the volume of the pyramid. Give your answer in cm³.
A92B891C297D594
4A cone has base radius $9$ cm and vertical height $12$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A13B15C7.94D21
5A cone has base radius $5$ cm and vertical height $12$ cm. Work out the volume of the cone. Give your answer in terms of $\pi$.
6A cylindrical tube has internal diameter $10$ cm and height $53$ cm. Balls of diameter $8$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A7B15C6D5
7A solid hemisphere and a solid cylinder both have radius $5$ cm. The cylinder has height $9$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A15 : 28B5 : 6C5 : 14D5 : 7
8A solid cone has base radius $6$ cm and slant height $12$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A1470B226C452D339
9A solid hemisphere has radius $8$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A402B804C201D603
10A pyramid has a square base of side $9$ cm and a volume of $270$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A90B3C270D10
11Two identical solid square-based pyramids each have a square base of side $3$ cm. Together they have a total volume of $54$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A18B27C3D9
12A solid cylinder has radius $7$ cm and height $15$ cm. A solid sphere has the same volume as the cylinder. Work out the radius of the sphere. Give your answer correct to 3 significant figures. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A8.20B9.02C23.5D13.0
13A solid cone has base radius $24$ cm and vertical height $10$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$, where $l$ is the slant height.)
A3620B2560C3770D1960
14The net of a cone is a sector of a circle of radius $18$ cm with an angle of $120°$ at the centre. The net is folded to make a cone of slant height $18$ cm. Work out the vertical height of the cone.
A6B17.0C12D19.0
15A solid is made from a cone on top of a cylinder. Both have base radius $r$ cm. The cone’s height is $3r$ cm and the cylinder’s height is $r$ cm. The total volume of the solid is $300$ cm³. Work out the value of $r$. Give your answer correct to 3 significant figures. (Volume of a cone $= \dfrac{1}{3}\pi r^2 h$.)
A3.63B2.52C4.15D6.91
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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
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1Choose the correct formula for the curved surface area of a hemisphere of radius r.
A$4\pi r^2$B$2\pi r^2$C$3\pi r^2$D$\pi r^2$
2A cone has base radius $7$ cm and vertical height $24$ cm. Work out the slant height $l$ of the cone. Give your answer in cm.
A23.0B31C25D26.0
3The diagram shows a solid square-based pyramid. The base is a square of side $10$ cm and each of the four triangular faces has a slant height of $8$ cm. Work out the total surface area of the pyramid.
A260B180C160D420
4A sphere has a radius of $7$ cm. Work out the surface area of the sphere. Give your answer correct to 3 significant figures. (Surface area of a sphere $= 4\pi r^2$.)
A2460B1440C616D154
5A sphere has radius $8$ cm. Work out the volume of the sphere. Give your answer in terms of $\pi$. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
6A sphere has a radius of $12$ cm. Work out the volume of the sphere.
A57900B603C3620D7240
7A cylindrical tube has internal diameter $12$ cm and height $61$ cm. Balls of diameter $10$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A5B6C7D13
8Two identical solid square-based pyramids each have a square base of side $6$ cm. Together they have a total volume of $360$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A15B5C30D90
9A pyramid has a square base of side $8$ cm and a volume of $320$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A15B120C5D320
10A solid hemisphere has radius $6$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A452B113C226D339
11A solid hemisphere and a solid cylinder both have radius $5$ cm. The cylinder has height $11$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A15 : 32B5 : 16C15 : 22D5 : 8
12A solid cylinder has radius $5$ cm and height $8$ cm. A solid sphere has the same volume as the cylinder. Work out the radius of the sphere. Give your answer correct to 3 significant figures. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A8.43B12.2C5.31D5.85
13VABCD is a pyramid with a square base ABCD of side $8$ cm. The apex V is directly above the centre X of the base. Each slant edge (such as VC) is $8$ cm. Work out the volume of the pyramid.
A171B0C121D362
14A solid cone has a vertical height of $15$ cm and a volume of $180\pi$ cm³. Work out the curved surface area of the cone. Give your answer correct to 3 significant figures. (Volume $= \dfrac{1}{3}\pi r^2 h$, curved surface area $= \pi r l$.)
A113B283C418D305
15A solid square-based pyramid has a base of side $8$ cm. A solid hemisphere has radius $4$ cm. The volume of the hemisphere is $50\%$ of the volume of the pyramid. Work out the perpendicular height of the pyramid. Give your answer correct to 3 significant figures. (Volume of a hemisphere $= \dfrac{2}{3}\pi r^3$.)
A6.28B25.1C4.19D12.6
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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1Choose the correct formula for the curved surface area of a hemisphere of radius r.
A$2\pi r^2$B$4\pi r^2$C$3\pi r^2$D$\pi r^2$
2A cone has base radius $10$ cm and slant height $12$ cm. Work out the curved surface area of the cone (the curved part only). Give your answer in terms of $\pi$. (Curved surface area of a cone $= \pi r l$.)
3A pyramid has a square base of side $12$ cm. The apex is directly above the centre of the base and the perpendicular height of the pyramid is $16$ cm. Work out the volume of the pyramid. Give your answer in cm³.
A768B160C1536D2304
4A sphere has radius $7$ cm. Work out the volume of the sphere. Give your answer in terms of $\pi$. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
5A cone has base radius $4$ cm and vertical height $15$ cm. Work out the slant height $l$ of the cone.
A14.5B16C19D15.5
6Two identical solid square-based pyramids each have a square base of side $6$ cm. Together they have a total volume of $336$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A84B14C28D5
7A cylindrical tube has internal diameter $14$ cm and height $57$ cm. Balls of diameter $10$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A16B4C5D6
8A solid hemisphere and a solid cylinder both have radius $10$ cm. The cylinder has height $9$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A15 : 19B10 : 19C20 : 19D5 : 3
9A pyramid has a square base of side $12$ cm and a volume of $528$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A4B528C132D11
10A sphere has a radius of $7$ cm. Work out the volume of the sphere.
A205B11500C718D1440
11A solid cone has base radius $10$ cm and slant height $18$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A1190B565C5970D880
12A sphere has a volume of $36\pi$ cm³. Work out the radius of the sphere. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$.)
A3B6C5D4
13A solid cone has base radius $8$ cm and vertical height $6$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$, where $l$ is the slant height.)
A251B452C402D352
14A solid square-based pyramid has a base of side $8$ cm. A solid hemisphere has radius $3$ cm. The volume of the hemisphere is $40\%$ of the volume of the pyramid. Work out the perpendicular height of the pyramid. Give your answer correct to 3 significant figures. (Volume of a hemisphere $= \dfrac{2}{3}\pi r^3$.)
A2.21B6.63C2.65D13.3
15A solid is made from a cone on top of a cylinder. Both have base radius $r$ cm. The cone’s height is $3r$ cm and the cylinder’s height is $2r$ cm. The total volume of the solid is $250$ cm³. Work out the value of $r$. Give your answer correct to 3 significant figures. (Volume of a cone $= \dfrac{1}{3}\pi r^2 h$.)
A3.63B2.07C2.98D5.15
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3A sphere has a radius of $9$ cm. Work out the surface area of the sphere. Give your answer correct to 3 significant figures. (Surface area of a sphere $= 4\pi r^2$.)
A254B4070C1020D3050
4A pyramid has a square base of side $12$ cm. The apex is directly above the centre of the base and the perpendicular height of the pyramid is $4$ cm. Work out the volume of the pyramid. Give your answer in cm³.
A384B576C192D148
5A cone has a base radius of $4$ cm and a vertical height of $19$ cm. Work out the volume of the cone.
A1270B955C79.6D318
6A hemisphere has a diameter of $22$ cm. Work out the volume of the hemisphere.
A22300B5580C2790D507
7Two identical solid square-based pyramids each have a square base of side $6$ cm. Together they have a total volume of $336$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A28B14C5D84
8A solid cone has base radius $9$ cm and slant height $13$ cm. Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A622B3560C368D877
9A cylindrical tube has internal diameter $9$ cm and height $31$ cm. Balls of diameter $5$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A30B3C6D7
10A solid hemisphere and a solid cylinder both have radius $6$ cm. The cylinder has height $14$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A9 : 20B3 : 5C3 : 10D9 : 14
11A pyramid has a square base of side $6$ cm and a volume of $72$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A2B72C36D6
12VABCD is a pyramid with a square base ABCD of side $12$ cm. The apex V is directly above the centre X of the base. Each slant edge (such as VC) is $11$ cm. Work out the volume of the pyramid.
A528B1010C336DNaN
13A solid cone has a vertical height of $12$ cm and a volume of $100\pi$ cm³. Work out the curved surface area of the cone. Give your answer correct to 3 significant figures. (Volume $= \dfrac{1}{3}\pi r^2 h$, curved surface area $= \pi r l$.)
A78.5B188C283D204
14The net of a cone is a sector of a circle of radius $15$ cm with an angle of $120°$ at the centre. The net is folded to make a cone of slant height $15$ cm. Work out the vertical height of the cone.
A15.8B5C10D14.1
15Two cones are joined base-to-base to make a solid. Both cones have base radius $r$ cm. One cone has slant height $3r$ cm and the other has slant height $5r$ cm. The total curved surface area of the solid is $250\pi$ cm². Work out the value of $r$. Give your answer correct to 3 significant figures. (Curved surface area of a cone $= \pi r l$.)
A4.08B31.3C5.00D5.59
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2The diagram shows a solid square-based pyramid. The base is a square of side $6$ cm and each of the four triangular faces has a slant height of $15$ cm. Work out the total surface area of the pyramid.
A126B396C216D180
3A sphere has a diameter of $22$ cm. Work out the surface area of the sphere. Give your answer correct to 3 significant figures. (Surface area of a sphere $= 4\pi r^2$.)
A6080B1520C380D5580
4A cone has a base radius of $6$ cm and a vertical height of $17$ cm. Work out the volume of the cone.
A1920B107C2560D641
5A cone has base radius $6$ cm and vertical height $9$ cm. Work out the volume of the cone. Give your answer in terms of $\pi$.
6A cylindrical tube has internal diameter $12$ cm and height $31$ cm. Balls of diameter $8$ cm are dropped in so they stack on top of one another. Work out the greatest number of whole balls that fit inside the tube.
A3B2C13D4
7A solid hemisphere and a solid cylinder both have radius $7$ cm. The cylinder has height $5$ cm. Work out the ratio of the total surface area of the hemisphere to the total surface area of the cylinder. Give your answer in its simplest form. (Curved surface area of a hemisphere $= 2\pi r^2$.)
A7 : 8B21 : 10C7 : 6D7 : 12
8A pyramid has a square base of side $10$ cm and a volume of $600$ cm³. The apex is directly above the centre of the base. Work out the perpendicular height of the pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A600B180C18D6
9A solid hemisphere has radius $9$ cm. Work out the total surface area of the solid hemisphere. Give your answer correct to 3 significant figures. (The curved surface area of a hemisphere is $2\pi r^2$.)
A509B1020C254D763
10A sphere has a radius of $5$ cm. Work out the volume of the sphere.
A105B524C4190D262
11Two identical solid square-based pyramids each have a square base of side $5$ cm. Together they have a total volume of $250$ cm³. Work out the perpendicular height of each pyramid. (Volume of a pyramid $= \dfrac{1}{3} \times \text{base area} \times \text{height}$.)
A5B30C15D75
12A sphere has a surface area of $400\pi$ cm². Work out the volume of the sphere. Give your answer correct to 3 significant figures. (Surface area $= 4\pi r^2$, volume $= \dfrac{4}{3}\pi r^3$.)
A3140B2090C1260D4190
13A solid sphere has radius $8$ cm. A solid cone has a height equal to its base diameter, and the cone has the same volume as the sphere. Work out the base diameter $d$ of the cone. Give your answer correct to 3 significant figures. (Volume of a sphere $= \dfrac{4}{3}\pi r^3$, volume of a cone $= \dfrac{1}{3}\pi r^2 h$.)
A25.4B12.7C16.0D20.2
14The net of a cone is a sector of a circle of radius $15$ cm with an angle of $216°$ at the centre. The net is folded to make a cone of slant height $15$ cm. Work out the vertical height of the cone.
A17.5B12.0C6D9
15Two cones are joined base-to-base to make a solid. Both cones have base radius $r$ cm. One cone has slant height $2r$ cm and the other has slant height $5r$ cm. The total curved surface area of the solid is $112\pi$ cm². Work out the value of $r$. Give your answer exactly. (Curved surface area of a cone $= \pi r l$.)
A4B3.35C3.53D16.0
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