Question

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere with same radius. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. (Take $\pi$ = 22/7)

• A. $296.11c{m}^3$
• B. $276.11c{m}^3$
• C. $266.11c{m}^3$
• D. $236.11c{m}^3$

Answer 1

Answer: (C)

$266.11c{m}^3$

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 $=\frac{1}{3}\pi r^{2}h$ 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 $=(\frac{2}{3}\times \frac{22}{7}\times {4.2}^3)+(\frac{1}{3}\times \frac{22}{7}\times {4.2}^2\times 6)=266.112{cm}^3$