VT · Surface Area & Volume: Cones, Spheres & Pyramids

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In each set, one thing changes and everything else stays the same. Work them out in order and look for the pattern — the last line tells you what to notice.

①Cone volume: only the radius changeschanging: the radius
Work out each volume to 3 s.f. The height is $6$ cm each time.
$r=3$ cm
Solid ()6 cm3 cm
=
$r=6$ cm
Solid ()6 cm6 cm
=
$r=9$ cm
Solid ()6 cm9 cm
=
The radius is SQUARED, so trebling $r$ multiplies the volume by $9$. Check: $3\to9$.
②Sphere volume: only the radius changeschanging: the radius
Work out each volume to 3 s.f.
$r=3$ cm
Solid ()3 cm
=
$r=6$ cm
Solid ()6 cm
=
$r=9$ cm
Solid ()9 cm
=
The radius is CUBED, so doubling $r$ multiplies the volume by $8$. Check: $3\to6$.
③Slant height: only the height changeschanging: the perpendicular height
Work out the slant height $l$ using $l^2=r^2+h^2$.
$r=5,\ h=12$
Solid ()125l
=
$r=6,\ h=8$
Solid ()86l
=
$r=9,\ h=12$
Solid ()129l
=
Each of these is a Pythagorean triple, so the slant height is a whole number.

Answers · Surface Area & Volume: Cones, Spheres & Pyramids

Variation practice
① Cone volume: only the radius changes
$r=3$ cm: 56.5 cm³$r=6$ cm: 226 cm³$r=9$ cm: 509 cm³
② Sphere volume: only the radius changes
$r=3$ cm: 113 cm³$r=6$ cm: 905 cm³$r=9$ cm: 3050 cm³
③ Slant height: only the height changes
$r=5,\ h=12$: 13 cm$r=6,\ h=8$: 10 cm$r=9,\ h=12$: 15 cm
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