Question

A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the conical base is 7 cm and the height of the toy is 14.5 cm. Find the volume of the toy

Answer 1

Diameter of hemisphere$=7$cm

Radius of hemisphere$r=d/2$

$=\frac{7}{2}=3.5$cm

Height of hemisphere$=$Radius of hemisphere

$=3.5$cm

Height of Toy$=14.5$cm

Height of cone$=14.5-3.5=11$cm

Radius of cone$=3.5$cm

$\therefore$ Volume of cone$=$Volume of cone$+$Volume of hemisphere

$=\frac{1}{3}\cdot \pi r^{2}h+\frac{4}{3}\cdot \pi r^3$

$=\frac{1}{3}\cdot \frac{22}{7}\cdot (3.5{)}^2\cdot 11+\frac{4}{3}\cdot \frac{22}{7}(3.5{)}^3$

Volume of toy$=320.83c{m}^3$.