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

1.	Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.
Answer» Curved surface area of sphere = 4πr² Let ‘r’ be the radius of sphere Height of cylinder =’ 2r’ Curved surface area of cylinder = 2πrh ⇒ 2πr(2r) ⇒ 4πr² ∴ Surface area of a sphere is equal to the curved surface area of the circumscribed cylinder

Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

Answer»

Curved surface area of sphere = 4πr²

Let ‘r’ be the radius of sphere

Height of cylinder =’ 2r’

Curved surface area of cylinder = 2πrh

⇒ 2πr(2r)

⇒ 4πr²

∴ Surface area of a sphere is equal to the curved surface area of the circumscribed cylinder