Question

The adjoining figure represents a solid consisting of a cylinder mounted by a cone at one end and a hemisphere at the other end. Given that, common radius $=3.5cm$, the height of the cylinder $=6.5cm$ and the total height $=12.8cm$, calculate the volume of the solid, correct to the nearest integer.

Answer 1

Height of core $=12.8-6.5-3.5=2.8cm$

Volume =Volume of cone + Volume of Cylinder +Volume of a hemisphere

$=\frac{1}{3}\times \frac{22}{7}\times (r{)}^2\times h+\frac{22}{7}\times (r{)}^2\times h+\frac{2}{3}\times \frac{22}{7}\times (r{)}^3$

$=\frac{1}{3}\times \frac{22}{7}\times (3.5{)}^2\times 2.8+\frac{22}{7}\times (3.5{)}^2\times 6.5+\frac{2}{3}\times \frac{22}{7}\times (3.5{)}^3$

$=35.93+250.25+89.83$

$=376.01c{m}^3$