Question

A solid wooden toy in the shape of a right circular cone is mounted on a hemisphere. 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.

• A. $104c{m}^3$
• B. $162c{m}^3$
• C. $427c{m}^3$
• D. $266c{m}^3$

Answer 1

The correct option is D $266c{m}^3$

Volume of the cone is given by = 1/3 $\times \pi r^{2}h$
Here r = 4.2 cm, h = 10.2 - r = 6 cm
Therefore the volume of the cone = 1/3 $\pi \times (4.2{)}^2\times 6cm=110.88c{m}^3$
Volume of the hemisphere $=\frac{1}{2}\times \frac{4}{3}\pi r^3=155.23c{m}^3$
Total volume = 110.88 + 155.232 = 266.112