Question

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the volume of the toy.

• A. $10266.67c{m}^3$
• B. $17266.67c{m}^3$
• C. $15266.67c{m}^3$
• D. $12266.67c{m}^3$

Answer 1

The correct option is A

$10266.67c{m}^3$

Volume of the toy = volume of the hemisphere + volume of the cone
Also since the cone is surmounted on a hemisphere, the volume of cone and that of hemisphere are equal.
We know that volume of hemisphere of radius 'r' is $\frac{2}{3}\pi r^3$ and volume of cone of radius 'r' and height 'h' is $\frac{1}{3}\pi r^{2}h$.

$Volume=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h$

$Volume=\pi r^2(\frac{2}{3}r+\frac{1}{3}h)$

$Volume=\frac{22}{7}\times 14\times 14(\frac{2}{3}\times 14+\frac{1}{3}\times 22)$

$Volume=22\times 2\times 14(\frac{28}{3}+\frac{22}{3})$

$Volume=22\times 2\times 14\times \frac{50}{3}$

$Volume=10266.67c{m}^3$