Question

A sphere,a cylinder and a cone are of the same radius and same height .find the ratio of their curved surface areas?

Answer 1

The standard formulae for respective curved areas are
Surface area of sphere 4πr^2
Area of lateral surface of cylinder 2πrh
Area of lateral surface of cone πr√(r^2 + h^2)

The height of a sphere is the diameter 2r. Since the cylinder and
cone are specified as the same height we substitute h = 2r

Specific formulae are now
Surface area of sphere 4πr^2
Area of curved surface of cylinder 2πr*2r = 4πr^2
Area of curved surface of cone πr√(r^2 + 4r^2) = πr^2√(5)

Dividing by 4πr^2 yields the ratio of their curved surfaces as
1: 1: √(5)/4 

Answer 2

Answer:

1:1:√[5]/4

Step-by-step explanation:

The standard formulae for respective curved areas are

Surface area of sphere 4πr^2

Area of lateral surface of cylinder 2πrh

Area of lateral surface of cone πr√(r^2 + h^2)

The height of a sphere is the diameter 2r. Since the cylinder and

cone are specified as the same height we substitute h = 2r

Specific formulae are now

Surface area of sphere 4πr^2

Area of curved surface of cylinder 2πr*2r = 4πr^2

Area of curved surface of cone πr√(r^2 + 4r^2) = πr^2√(5)

Dividing by 4πr^2 yields the ratio of their curved surfaces as

1: 1: √(5)/4