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Question

Two similar cones have volumes 12π cu. units and 96π cu. units. If the curved surface area of the smaller cone is 15π sq. units, what is the curved surface area of the larger one?

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Solution

Small cone volume 13πr21h1=12π
Large cone volume 13πr22h2=96π
[Similar cones r1r2=h1h2]
13πr21h113πr22h2=12π96π
r21r22=18×h2h1 [h2h1=r2r2]
r21r22=18×r2r1
r31=8r32
r1=2r2
Given surface area of smaller cone πr1r21+h2+πr21=15π
Large cone =πr22+πr2r22+h22
=π(2r1)2+π(2r1)(2r1)2+(2h1)2
4πr21+π2r1×2r21+h21
4(πr21+πr1r21+h21)=4×15π
60π.

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