Question

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is H cm and the diameter of the cylinder is 2 r cm. The volume of the solid is

• A. $\pi r^2(H-\frac{2r}{3})c{m}^3$
• B. $\pi r^2(H+\frac{2r}{9})c{m}^3$
• C. $\pi r^2(H-\frac{2r}{9})c{m}^3$
• D. $\pi r(H-\frac{2r}{3})c{m}^3$

Answer 1

The correct option is A $\pi r^2(H-\frac{2r}{3})c{m}^3$

Volume of solid = volume of cylinder + volume of two hemispheres
$=\pi r^{2}h+2\left(\frac{2}{3}\pi r^3\right)$
$=\pi r^2[h+\frac{4r}{3}]$

$=\pi r^2[H-2r+\frac{4r}{3}]$
$=\pi r^2[H-\frac{2r}{3}]$