Question

A hemispherical bowl is made of steel $0.25cm$ thick. The inside radius of the bowl is $5cm$. Find the volume of steel used in making the bowl.

Answer 1

Step 1: Find the outer radius of the hemispherical bowl.

Given that,

the inside radius $r$ of the bowl $=5cm$

The thickness of the steel $=0.25cm$

Therefore, the outer radius $R$ of the bowl $=5+0.25$

$=5.25cm$

Step 2: Find the volume of steel used in making the bowl.

We have, Volume of the steel making the bowl $=$ Volume of the hemispherical bowl

The volume of the hemispherical bowl of outer radius $R$ and inner radius $r$ $=\frac{2}{3}\pi (R^3-r^3)$

The volume of the steel $=\frac{2}{3}\pi \left(R^3-r^3\right)$

$$\begin{gathered} =\frac{2}{3}\times \frac{22}{7}({\left(5.25\right)}^3-5^3)(\mathrm{\pi }=\frac{22}{7}) \\ =\frac{2}{3}\times \frac{22}{7}(144.7-125) \\ =\frac{2}{3}\times \frac{22}{7}\times 19.7 \\ =41.28c{m}^3 \end{gathered}$$

Hence, the volume of the steel used in the bowl is $41.28c{m}^3$