Question

The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

• A. $225200\pi c{m}^3$
• B. $105000\pi c{m}^3$
• C. $115200\pi c{m}^3$
• D. $15200\pi c{m}^3$

Answer 1

The correct option is C

$115200\pi c{m}^3$

Given that the diameter of a football is 24 cm.
$⟹Radiusofthefootball=\frac{24}{2}=12cm$

Volume of air inside a football = Volume of the sphere of radius $12cm$

Note that the volume of a sphere of radius $r=\frac{4}{3}\pi r^3$

Thus, volume of the sphere of radius $12cm$
$=\frac{4}{3}\pi (12{)}^3=2304\pi c{m}^3$

Volume of air inside 50 such footballs
$=50\times \text{Volume of air inside a football}=50\times 2304\pi =115200\pi c{m}^3$