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 :

Answer: Option B

Solution

Answer: Option B

Solution:

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