A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14·5 cm. Then the volume of the toy is ($\pi = \frac{22}{7}$)

Explanation

Given that– Diameter of Hemisphere = 7 cm Total height of the toy = 14.5 cm Now Diagram of a cone mounted on a hemisphere Total volume of the toy = Volume of the Hemisphere + Volume of the cone. Total volume = $\frac{2}{3}\pi r^3 + \frac{1}{3}\pi r^2rh$ = $\frac{\pi}{3}r^2(2r + h)$ = $\frac{22}{7 \times 3} \times \frac{7}{2} \times \frac{7}{2} \left( 2 \times \frac{7}{2} + 11 \right)$ = $\frac{22}{3} \times \frac{7}{4} \times 18$ = $11 \times 21$ [<mark>Total volume = 231 cm²</mark>]