Question

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

• A. 144 cm³
• B. 132 cm³
• C. 154 cm³
• D. 169 cm³

Answer 1

The correct option is C

154 cm³

We know that,
volume of cone $=\frac{1}{3}\pi r^{2}h$
volume of hemisphere $=\frac{2}{3}\pi r^3$

Total volume
= Volume of the cone + Volume of the hemisphere

$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3=\frac{1}{3}\pi r^2(h+2r)=\frac{1}{3}\times \frac{22}{7}\times {3.5}^2\times (5+7)=\frac{1}{3}\times \frac{22}{7}\times {3.5}^2\times 12=22\times 0.5\times 3.5\times 4=154{\text{cm}}^3$

$\therefore$ The volume of the solid formed is
$154{\text{cm}}^3$