Question

The outer diameter of a hollow iron sphere of thickness $1cm$ is $12cm$. Find the volume of iron used to make the sphere.

• A. $1144{cm}^3$
• B. $381.33{cm}^3$
• C. ​​​​​​​$762.66{cm}^3$
• D. ​​​​​​​​​​​​​​$572{cm}^3$

Answer 1

The correct option is B $381.33{cm}^3$

$\text{Thickness of the iron = 1 cm}$

$\text{Outer radius}=6cm$
$\text{Hence, outer volume of the sphere}$
$=\frac{4}{3}$ $\pi$ $(r_{outer}{)}^3$
$=\frac{4}{3}$ $\pi$ $(6{)}^3$
$=905.143{cm}^3$

$\text{Inner radius}=5cm$
$\text{Therefore, inner volume of the sphere}$
$=\frac{4}{3}$ $\pi$ $(r_{inner}{)}^3$
$=\frac{4}{3}$ $\pi$ $(5{)}^3$
$=523.809{cm}^3$

Then, volume of iron used
= Outer volume – Inner volume
$=381.33{cm}^3$