Question

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

• A. $2\pi c{m}^3$
• B. $8\pi c{m}^3$
• C. $7\pi c{m}^3$
• D. $\pi c{m}^3$

Answer 1

The correct option is D $\pi c{m}^3$

Area of solid $=$ Area of cone $+$ area of cone

Radius $=1$cm
Height $=1$cm
Volume of Hemisphere
$=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\pi \times 1^3$
$=\frac{2}{3}\pi c{m}^2$
Volume of cone is,
$\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi \times 1^2\times 1$
$=\frac{1}{3}\pi c{m}^2$
$\therefore$ total Volume $=\frac{2}{3}\pi +\frac{1}{3}\pi$
$=\pi \left(\frac{2+1}{3}\right)$
$=\pi c{m}^3$