Question

The surface area of a sphere is 154 cm². The volume of the sphere is
(a) $179\frac{2}{3}{\mathrm{cm}}^3$
(b) $359\frac{1}{3}{\mathrm{cm}}^3$
(c) $1437\frac{1}{3}{\mathrm{cm}}^3$
(d) None of these

Answer 1

(a) $179\frac{2}{3}{\mathrm{cm}}^3$
Surface area of a sphere$=4\mathrm{\pi }{r}^2$
Therefore,
$$\begin{gathered} 4\mathrm{\pi }{r}^2=154 \\ \Rightarrow 4\times \frac{22}{7}\times r^2=154 \\ \Rightarrow r^2=\left(154\times \frac{7}{88}\right) \\ \Rightarrow r^2=\frac{49}{4} \\ \Rightarrow r^2={\left(\frac{7}{2}\right)}^2 \\ \Rightarrow r=\frac{7}{2}\text{cm} \end{gathered}$$
Volume of the sphere$=\frac{4}{3}\mathrm{\pi }{r}^3$
$$\begin{gathered} =\left(\frac{4}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}\right){\text{cm}}^3 \\ =\frac{539}{3}{\text{cm}}^3 \\ =179\frac{2}{3}{\text{cm}}^3 \end{gathered}$$