Question

What will be the diameter of the sphere whose surface area is $616{\text{cm}}^2$?

• A. $7\text{cm}$
• B. $14\text{cm}$
• C. $28\text{cm}$
• D. $14\sqrt{2}\text{cm}$

Answer 1

The correct option is B $14\text{cm}$

The figure of a sphere with centre at $O$ and diameter $AB$ can be depicted as follows:


It can be clearly observed that the radius is half the diameter, i.e., $r=\frac{d}{2}$, where $r$ is the radius and $d$ is the diameter of sphere.

The formula used to calculate the surface area of the sphere is $4\pi r^2$. It is given that the surface area is $616{\text{cm}}^2$, therefore the radius of sphere can be calculated as

$\begin{array}{cc}\text{Surface area of sphere}& =4\pi r^2\\ 616& =4\left(\frac{22}{7}\right)r^2\\ r^2& =\frac{616}{4}\times \frac{7}{22}\\ r^2& =49\\ r& =7\end{array}$

Substitute the value of $r$ in the formula $r=\frac{d}{2}$, to obtain the value of diameter of sphere, i.e.,
$$\begin{array}{cc}7& =\frac{d}{2}\\ d& =7\times 2\\ & =14\end{array}$$
Hence, the diameter of the given sphere is $14\text{cm}$.