Question

two similar cones have volumes 12 π cubic units and 96π cubic units if the curved surface area of smaller cone is 15π square units what is the curved surface area of larger cone
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Answer 1

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Let  R = radius of base and L = lateral height,  H = height of cone.curved surface or lateral surface = A =  π R L ,  and    volume = V = π/3* R² H,Similar cones have the same (cone) angle at the apex.  Hence the same ratios among R,  H and L.   Let Cone 1 be the larger cone.        Let  R₂ = x R₁,  H₂ = x H₁  and  L₁ = x L₂       V₁ / V₂ = π R₁² H₁ / π R₂² H₂  = x³ = 96 π / 12 π  = 8                   Hence  x = 2       Lateral Surface areas A₁ / A₂ = π R₁ L₁ / π R₂ L₂   =  x²  = 4 ,    as x = 2     A₁ = 4 A₂ = 4  * 15 π = 60 π square units.

Answer 2

Refer to the Attachment ✌️