Question

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 $c{m}^3$ and its diameter is 7 cm, find the height of the toy.

Answer 1

Given:

Volume of toy=231 $c{m}^3$

Diameter of a hemisphere= 7 cm

radius of hemisphere = radius of cone = 3.5 cm

Height of hemisphere= radius of hemisphere= 3.5 cm

Let $h$ be the height of toy

Volume of toy = volume of cone + volume of hemisphere

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

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

$231=\left(\frac{22}{7}\right)\times (3.5{)}^2\times (\frac{1}{3}\left)\right(h+2\times 3.5)$

$231\times 3=\frac{(22\times 3.5\times 3.5)}{7}(h+7)$

$h+7=\frac{(231\times 3\times 7)}{(3.5\times 3.5\times 22)}$

$\therefore$ $h+7=18=11$ cm

Hence, the height of the toy = 11 cm