Question

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

• A. $10266.66{\text{cm}}^3$
• B. $17266.67{\text{cm}}^3$
• C. $15266.67{\text{cm}}^3$
• D. $12266.67{\text{cm}}^3$

Answer 1

The correct option is A

$10266.66{\text{cm}}^3$

The volume of the toy = volume of hemisphere + volume of a cone

$V=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^{2}h=\frac{2}{3}\times \frac{22}{7}(14{)}^3+\frac{1}{3}\times \frac{22}{7}(14{)}^2\left(22\right)=\frac{2}{3}\times 22\times 2\times 14\times 14+\frac{1}{3}\times 22\times 2\times 14\times 22=\frac{1}{3}[2\times 22\times 2\times 14\times 14+22\times 2\times 14\times 22]=\frac{1}{3}[17248+13552]=\frac{1}{3}\times 30800V=10266.66{\text{cm}}^3$

$\therefore$ Volume of the toy = $10266.66{\text{cm}}^3$