Question

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is :

A. 4πr³ 

B. \(\frac{8}{3}\)πr³ 

C. 2πr³ 

D. 8πr³

Answer 1

Option : (C)

Volume of a sphere = \(\frac{4}{3}\)πr³ 

Volume of a cylinder = πr²h 

Given, 

sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder and the radius of the sphere is r 

Thus, 

height of the cylinder = diameter = 2r and base radius = r 

Volume of the cylinder = π × r² × 2r 

= 2πr³