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Question

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8:5, determine the ratio of the radius of the base to the height of either of them.

Solution
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CSAofcylinderCSAofcone=85
2πrhπrl=85hl=455h=4l5h=4h2+r2
Squaring both sides, we get
25h2=16(h2+r2)9h2=16r2h2r2=169
hr=169=43=4:3orrh=34=3:4

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