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.