Question

find the volume of sphere whose surface area is 154 cm square

Answer 1

$$\begin{gathered} \mathrm{Let}r=\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{sphere} \\ \mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sphere}=154{\mathrm{cm}}^2 \\ \Rightarrow 4\mathrm{\pi }{r}^2=154 \\ \Rightarrow 4\times \frac{22}{7}\times r^2=154 \\ \Rightarrow r^2=\frac{154\times 7}{22\times 4}=\frac{49}{4} \\ \Rightarrow r\mathit{}=\frac{7}{2}\mathrm{cm} \\ \mathrm{now},\mathrm{volume}\mathrm{of}\mathrm{sphere}=\frac{4}{3}\mathrm{\pi }{r}^{\mathit{3}}=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^3 \\ =\frac{539}{3}=179.67{\mathrm{cm}}^3 \end{gathered}$$