Question

Example 11: A solid wooden toy is in the shape o right circular cone mounted on a hemisphere. If radius of the hemisphere is 4.2 cm and the total hei of the toy is 12.2 cm, find the volume of the woo toy.​

Answer 1

Volume of the toy = Volume of the hemispherical part + Volume of conical part

Volume of a hemisphere of radius 'r' =  $\frac{2}{3} \pi r^{3}$

Volume of a cone = $\frac{2}{3}\pi r^{2}h$ where r

is the radius of the base of the cone and h is the height.

The hemisphere and the cone will have the same radius r = 4.2cm

Since total length of the toy is 10.2 cm, the length of the conical part will be 10.2 − 4.2=6cm

Hence, Volume of the solid = $( \frac{2}{3} * \frac{22}{7} * 4.2^{3}) + (\frac{1}{3} * \frac{22}{7} * 4.2^{2} * 6)$

= 266.112cm³

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