Question

Area of the base of a solid hemisphere is 36$\pi c{m}^2$. Then its volume is :

• A. $288\pi c{m}^3$
• B. $108\pi c{m}^3$
• C. $144\pi c{m}^3$
• D. $72\pi c{m}^3$

Answer 1

The correct option is C $144\pi c{m}^3$

Let the radius of the hemisphere be ${}^{\prime }{r}^{\prime }$ cm.

Area of base $=36\pi {cm}^2$

$\Rightarrow \pi r^2=36\pi$

$\Rightarrow r^2=36$

$\Rightarrow r=6cm$

$\therefore$ Volume of hemisphere $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \pi \times 6\times 6\times 6$

$=144\pi {cm}^3$