Question

write the solution step by step.

Answer 1

correct one............

Answer 2

Step-by-step explanation:

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.