Question

The outer and inner diameters of a spherical shell are $10cm$and $9cm$respectively. Find the volume of metal contained in it. (Take $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1. Given measures of the spherical shell

The outer diameter of the spherical shell $=10cm$

The inner diameter of the spherical shell $=9cm$

Step 2. Finding the radius of the spherical shell

The outer radius of the spherical shell $=\frac{10}{2}=5cm$

The inner radius of the spherical shell $=\frac{9}{2}=4.5cm$

Step 3. Finding the volume of the cylinder

The volume of the metal contained in the shell

$$\begin{gathered} =\frac{4}{3}{\mathrm{\pi R}}^3-\frac{4}{3}{\mathrm{\pi r}}^3 \\ =\frac{4}{3}\mathrm{\pi }{\left(5\right)}^3-\frac{4}{3}\mathrm{\pi }{(4.5)}^3=\frac{4}{3}\mathrm{\pi }(125-91.125) \\ =\frac{4}{3}\times \frac{22}{7}\times 33.875 \\ =1.3\times 3.14\times 33.875 \\ =138.277c{m}^3 \end{gathered}$$

Hence, the volume of the metal contained in the shell is $138.277c{m}^3$.