Question

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

Answer 1

Sol:
Let the radius of the sphere = r
Surface area of the sphere = 4πr²
Radius of the cylinder circumscribed over the sphere = r
Height of the cylinder circumscribed over the sphere (h) = 2r
Curved surface area of the cylinder = 2πrh
= 2πr(2r)
= 4πr²
Therefore, the curved surface area of the circumscribed cylinder over a sphere is equal to the surface area of the sphere.