Question

The inner radius of a hollow iron sphere is $9cm$. If the iron is $1cm$ thick, find the volume of iron used in the sphere.

• A. 1155.08 cm³
• B. 1156.08 cm³
• C. 1134.59 cm³
• D. 1133.58 cm³

Answer 1

The correct option is C

1134.59 cm³

Thickness of the iron = 1 cm
Inner radius = 9 cm
Therefore, inner volume of sphere =$\frac{4}{3}$ $\pi$ $(r_{inner}{)}^3$
$=\frac{4}{3}$ $\times$ $\pi$ $\times$ $(9{)}^3$
$=3052.08{cm}^3$

Outer radius = 10 cm
Outer volume = $\frac{4}{3}$ $\times$ $\pi$ $\times$ $(r_{outer}{)}^3$
$=\frac{4}{3}$ $\pi$ $(10{)}^3$
$=4186.67{cm}^3$
Then, iron used = Outer volume – Inner volume
$=1134.59{cm}^3$