Question

Two similiar cones have volumes 12 rt cu. units and 96 cu units. If
the curved surface area of the smaller cone is 1570 sq. units, what is
the curved surface area of the larger one?​

Answer 1

Answer:

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.