Each example shows a little less than the one before – complete the faded steps yourself, using the same three steps every time: write the formula, substitute $r$ and $h$, then evaluate to 3 s.f. Also answer the check question. Calculator; use the $\pi$ button.
①Example 1fully worked: read it through
Work out the volume of a cone with radius $3$ cm and height $7$ cm.
1Write $V=\tfrac13\pi r^2 h$
$V=\tfrac13\pi r^2 h$
2Substitute $r$ and $h$
$V=\tfrac13\pi(3)^2(7)=21\pi$
3Evaluate to 3 s.f.
$=66.0$ cm$^3$
Check · Which measurement is squared in the formula?
A the height $h$B the radius $r$C both $r$ and $h$D neither
②Example 2you finish the last 1 step
Work out the volume of a cone with radius $4$ cm and height $9$ cm.
1Write $V=\tfrac13\pi r^2 h$
$V=\tfrac13\pi(4)^2(9)$
2Substitute $r$ and $h$
$=48\pi$
3Evaluate to 3 s.f.
$=151$ cm$^3$
Check · Why is there a $\tfrac13$ in the formula?
A a cone has one third the volume of the cylinder with the same base and heightB because there are three dimensionsC to make it a fractionD it should be $\tfrac12$
③Example 3you finish the last 2 steps
Work out the volume of a cone with radius $5$ cm and height $6$ cm.
1Write $V=\tfrac13\pi r^2 h$
$V=\tfrac13\pi(5)^2(6)$
2Substitute $r$ and $h$
$=50\pi$
3Evaluate to 3 s.f.
$=157$ cm$^3$
Check · What is $\tfrac13\pi(25)(6)$ as a multiple of $\pi$?
A $150\pi$B $50\pi$C $450\pi$D $25\pi$
④Example 4your turn: every step
Work out the volume of a cone with radius $6$ cm and height $10$ cm.
1Write $V=\tfrac13\pi r^2 h$
$V=\tfrac13\pi(6)^2(10)$
2Substitute $r$ and $h$
$=120\pi$
3Evaluate to 3 s.f.
$=377$ cm$^3$
Check · The height given is the perpendicular height. Which height would be WRONG to use here?
A the perpendicular heightB the slant heightC the radiusD the diameter
Answers · Surface Area & Volume: Cones, Spheres & Pyramids
Faded examples · Finding the volume of a cone
① Example 1$V=\tfrac13\pi r^2 h$→$V=\tfrac13\pi(3)^2(7)=21\pi$→$=66.0$ cm$^3$$66.0\text{ cm}^3$
Check: B: the radius $r$
② Example 2$V=\tfrac13\pi(4)^2(9)$→$=48\pi$→$=151$ cm$^3$$151\text{ cm}^3$
Check: A: a cone has one third the volume of the cylinder with the same base and height
③ Example 3$V=\tfrac13\pi(5)^2(6)$→$=50\pi$→$=157$ cm$^3$$157\text{ cm}^3$
Check: B: $50\pi$
④ Example 4$V=\tfrac13\pi(6)^2(10)$→$=120\pi$→$=377$ cm$^3$$377\text{ cm}^3$
mathedup.co.uk · sheet IOAE