A solid body is made up of a cylinder of radius r and height r, a cone of base radius r and height r fixed to the cylinder's one base and a hemisphere of radius r to its other base. The total volume of the body (given r = 2) is :

A. 8π

B. 16π

C. 32π

D. 64π

Answer: Option B

Solution(By Examveda Team)

Total volume of the body :
= Volume of the cylinder + Volume of the cone + Volume of the hemisphere
$$\eqalign{ & = \pi {r^2}.\,r + \frac{1}{3}\pi {r^2}.\,r + \frac{2}{3}\pi {r^3} \cr & = 2\pi {r^3} \cr & = 2\pi {\left( 2 \right)^3} \cr & = 16\pi \cr} $$