Question

Find the volume of a sphere whose surface area is 154 cm2.

Answer 1

Let the radius of the sphere be r.
Surface area of sphere = 4$\pi$r2 = 154 cm2
Volume of a sphere = $\frac{4}{3}\pi$r3
$⇒$ Surface area of the sphere = 4$\pi$r2 = 154cm²
r2 = $\frac{154\ cm^2 }{ 4\pi}$

r2 = (154 cm2) $÷$ (4 × $\frac{22}{7}$)

r = $\sqrt{\frac{49}{4}}$cm²

r = $\frac{7}{2}$ cm

Now, radius of the sphere = $\frac{7}{2}$ cm

So, volume of the sphere = $\frac{4}{3}\pi$r3

= $\frac{4}{3}$ × $\frac{22}{7}$ × $\frac{7}{2}$ cm × $\frac{7}{2}$ cm × $\frac{7}{2}$ cm

= $\frac{539}{3}$ cm3

Therefore, volume of the sphere is $\frac{539}{3}$ cm3.