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 ⇒πr1√r21+h2+πr21=15π