Optional extension: Cones, hollow solids and changing dimensions
Example 1
A right circular cone has radius 12cm and slant height 13cm. Find its volume. Use V=3πr2h, where h is the perpendicular height, and π=3.
Right circular coneDiagram not to scaleShow worked answer
Answer: 720
Pythagoras gives h2=132−122
h=5.
Then V=122×5=720cm3.
Example 2
An open hollow pipe has outer radius 5cm, inner radius 3cm and height 5cm. Find its total surface area, including both ring-shaped ends and both curved surfaces. Use π=3.
Open hollow pipeDiagram not to scaleShow worked answer
Answer: 336
Add outer and inner curved areas 2π(R+r)h, plus two end rings 2π(R2−r2).
With π=3 the total is 336cm2.
Example 3
A right circular cone has radius 16cm and slant height 34cm. Find its volume. Use V=3πr2h, where h is the perpendicular height, and π=3.
Right circular coneDiagram not to scaleShow worked answer
Answer: 7680
Pythagoras gives h2=342−162
h=30.
Then V=162×30=7680cm3.
Composite Solids I practice | Year 11 | Ascent Arcade