Question

Find the volume of a sphere whose surface area is $55.44{cm}^2$. (Take $\pi =\frac{22}{7}$)

• A. $38.808{cm}^3$
• B. $38.008{cm}^3$
• C. $32.808{cm}^3$
• D. $28.808{cm}^3$

Answer 1

The correct option is A $38.808{cm}^3$

Let $r$ cm be the radius of the sphere. Its surface area $=55.44{cm}^2$
$\Rightarrow$ $4\pi r^2=55.44$
$\Rightarrow$ $4\times \frac{22}{7}\times r^2=55.44$
$\Rightarrow$ $r^2=\frac{55.44\times 7}{4\times 22}=4.41={\left(2.1\right)}^2$
$\Rightarrow$ $r=2.1cm$
now, volume of the sphere$=\frac{4}{3}\pi r^3=\frac{1}{3}\left(4\pi r^2\right)\times r=\frac{1}{3}\times 55.44\times 2.1{cm}^3$
$=55.55\times 0.7{cm}^3$
Hence the volume of the sphere $=38.808{cm}^3$