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 (assume $\pi =3.14$).

• A. $3052.08c{m}^3$​
• B. $3051.08c{m}^3$​
• C. $3053.08c{m}^3$​
• D. $3054.08c{m}^3$​

Answer 1

The correct option is A $3052.08c{m}^3$​

Surface area of the sphere
$\Rightarrow 4\pi$ $r^2=1256c{m}^2$
$\Rightarrow 4\times 3.14\times r^2=1256c{m}^2$
$\Rightarrow r=10cm$

Thickness of the iron = 1 cm.
So, inner radius $R$= 9 cm.

Therefore,
volume of air = inner volume of sphere
$=\frac{4}{3}$ $\times$$\pi$ $\times$ $R^3$

$=\frac{4}{3}\times 3.14\times 9^3$

$=3052.08c{m}^3$​