Question

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If thickness of iron is $1cm$, find the volume of air filled inside the ball.

• A. 3052.08 cm³
• B. 3051.08 cm³
• C. 3053.08 cm³
• D. 3054.08 cm³

Answer 1

The correct option is A 3052.08 cm³

$\text{Surface area of the sphere = 4}$$\pi$ $r^2$ $=1256m^2$
$\Rightarrow 4$ $\times$ $3.14\times$ $r^2=1256c{m}^2$
$\Rightarrow r=10cm$
$\text{Thickness of the iron = 1cm}$
$\text{So, inner radius = 9 cm}$

$\text{Therefore, volume of air = inner volume of sphere}$
$=\frac{4}{3}$ $\times$$\pi$ $\times$ $r^3$
$=\frac{4}{3}$ $\times$ $\pi$ $\times$ $9^3$
$=3052.08c{m}^3$​