Question

Find the radius of a sphere whose surface area is $154{\mathrm{cm}}^2$. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Compute radius of the given sphere

Given, surface area of the sphere $=154{\mathrm{cm}}^2$ and $\mathrm{\pi }=\frac{22}{7}$.

Formula for surface area of a sphere is,

$\mathrm{A}=4{\mathrm{\pi r}}^2$

where, $\mathrm{A}$ is the surface area and $\mathrm{r}$ is the radius of the sphere.

Thus, substituting the values,

$$\begin{gathered} 154=4·\frac{22}{7}·{\mathrm{r}}^2 \\ \Rightarrow {\mathrm{r}}^2=\frac{154\times 7}{4\times 22} \\ \Rightarrow {\mathrm{r}}^2=12.25 \\ \Rightarrow \mathrm{r}=3.5\mathrm{cm} \end{gathered}$$

Therefore, the radius of the sphere is $3.5\mathrm{cm}$.