Question

Note Take $\mathrm{\pi }=\frac{22}{7}$, unless stated otherwise.
Find the volume of a sphere whose surface area is 154 cm².

Answer 1

Let the radius of the sphere be r cm.

Surface area of the sphere = 154 cm²

$$\begin{gathered} \therefore 4\mathrm{\pi }{r}^2=154 \\ \Rightarrow 4\times \frac{22}{7}\times r^2=154 \\ \Rightarrow r=\sqrt{\frac{154\times 7}{4\times 22}}=\sqrt{12.25} \\ \Rightarrow r=3.5\mathrm{cm} \end{gathered}$$
∴ Volume of the sphere = $\frac{4}{3}\mathrm{\pi }{r}^3=\frac{4}{3}\times \frac{22}{7}\times {\left(3.5\right)}^3\approx 179.67{\mathrm{m}}^3$

Thus, the volume of the sphere is approximately 179.67 m³.