Question

The area of the circle is $154{\text{cm}}^2$. If the radius of the sphere is same as the radius of the circle, then what will be the volume of the sphere?

NOTE: Take the value of $\pi =\frac{22}{7}$

• A. $1437.33{\text{cm}}^3$
• B. $205.33{\text{cm}}^3$
• C. $4312{\text{cm}}^3$
• D. $1437.33{\text{cm}}^2$

Answer 1

The correct option is A $1437.33{\text{cm}}^3$

Assume the radius of the circle be $r$ and let it be shown as follows:


The formula used to calculate the area of the circle is $\pi r^2$. Given, the area of circle is $154{\text{cm}}^2$, therefore substitute the value of area to find the radius of circle.

$\begin{array}{cc}\text{Area of circle}& =\pi r^2\\ 154& =\left(\frac{22}{7}\right)r^2\\ r^2& =154\times \frac{7}{22}\\ r^2& =49\\ r& =7\end{array}$

Thus, the radius of the circle is $7\text{cm}$.

It is given that the radius of the sphere is same as that of circle, thus the figure of sphere can be represented as:


And the volume of sphere can be calculated as follows:

$\begin{array}{cc}\text{Volume of sphere}& =\frac{4}{3}\pi r^3\\ & =\frac{4}{3}\left(\frac{22}{7}\right)\left(7^3\right)\\ & =\frac{30184}{21}\\ & =1437.33\end{array}$

Hence, the volume of sphere is $1437.33{\text{cm}}^3$.