Question

Prove that the surface area of a sphere is equal to the curved surface area of the circumference cylinder__?

Answer 1

Let radius of a sphere be r

Curved surface area of sphere = 4πr²

S₁ = 4πr²

Let radius of cylinder be 'r 'cm

Height of cylinder be '2' r cm

Curved surface area of cylinder = 2πrh

S₂ = 2πr(2r) = 4πr²

S₁ and S₂ are equal. Hence proved

So curved surface area of sphere = surface area of cylinder