Question

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.$[Use=\frac{22}{7}]$

Answer 1

Let r and h be radius and height of the cone respectively.
Radius of cone (r) = 7 cm (Given)
Diameter of cone = $2\times r=(2\times 7)cm=14cm$

According to the question, height of the cone is equal to its diameter
$\therefore$ Height of cone (h) =14 cm
Radius of hemisphere =Radius of cone =7 cm
$\therefore$ Volume of soild =Volume of cone +Volume of hemisphere
$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3=\frac{\pi r^2}{3}[h+2r]=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times [14+(2\times 7\left)\right]c{m}^3=\frac{22}{3}\times 7\times 28c{m}^3=\frac{4312}{2}c{m}^3=1437.33c{m}^3$
Thus, the volume of the solid is 1437.33 $c{m}^3$.