Find the volume of a sphere whose surface area is 154 \({cm}^2\) .

Given :
Surface area of sphere = 154 \({cm}^2\).
Let radius of sphere be r.

But, we also know that,
Surface area of sphere = \(4{\pi}{r}^2\)
\(\Rightarrow \) 154 \({cm}^2\)= \(4 × \frac{22}{7} × {r}^2\)
\(\Rightarrow \) \({r}^2 = (\frac{154 × 7}{4 × 22})\) \({cm}^2\)
\(\Rightarrow \) r = \(\frac{7}{2} cm\)
\(\Rightarrow \) r = 3.5 cm

Now, Volume of sphere
= \(\frac{4}{3}{\pi}{r}^3\)
= \(\frac{4}{3} × \frac{22}{7} × {3.5}^3\) \({cm}^3\)
= \(179\frac{2}{3}\) \({cm}^3\)

Therefore , the volume of the sphere is
= \(179\frac{2}{3}\) \({cm}^3\).