Question

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

Answer 1

Answer:

60 π square units.

Step-by-step explanation:

Hey Mate,

Let,

•R = radius of base

•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 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  

•L₁ = x L₂

So,

●V₁ / V₂ = (π R₁² H₁) / (π R₂² H₂ )

•=> x³ = 96 π / 12 π 

•=> x³ = 8

Hence  x = 2 

●Lateral Surface areas

A₁ / A₂ = (π R₁ L₁) / (π R₂ L₂) 

=>  x²  = 4   

=> x = 2

A₁ = 4

A₂ = 4 × 15 π = 60 π square units.

HOPE ITS HELP YOU.

THANK-YOU

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