Question

The inner diameter of a cylindrical container is $7\text{cm}$ and its top is of the shape of a hemisphere. If the shape of a hemisphere. If the height of the container is $16\text{cm}$, then find the actual capacity of the container. Use $\pi =\frac{22}{7}$

Answer 1

Radius, $r=\frac{7}{2}=3.5\text{cm}$

Height of cylinder $h=16-3.5=12.5\text{cm}$

So,

Volume of cylinder $=\pi r^{2}h$

$=\frac{22}{7}\times (3.5{)}^2\times 12.5$

$=481.25{\text{cm}}^3$

And,

Hemisphere volume $=\frac{2}{3}\times \pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times (3.5{)}^2$

$=89.79{\text{cm}}^3$

Total capacity $=481.25+89.79$

$=571.04{\text{cm}}^3$