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. $4\pi r^3$
  
• B. $\frac{8}{3}\pi r^3$
  
• C. $2\pi r^3$
  
• D. $8\pi r^3$
  

Answer 1

The correct option is C

$2\pi r^3$

Radius of sphere $=r$

$\therefore Volume=\frac{4}{3}\pi r^3$
$\therefore$ Radius of cylinder $\left(R\right)=r$
and height $\left(h\right)=2r\therefore Volume=\pi R^{2}H=\pi r^2\times 2r=2\pi r^3$