Question

The area of a circle is 154 square centimeters. If the radius of the sphere is the same as the radius of the circle, then what will the volume of the sphere be?

(Note: $\pi =\frac{22}{7}$)

• A. 1437.33 cu cm
• B. 4312 cu cm
• C. 205.33 cu cm
• D. 1437.33 cu cm

Answer 1

The correct option is A 1437.33 cu cm

Assume that the radius of the circle is $r$ and let it be represented as follows:


The formula used to calculate the area of the circle is $\pi r^2$. Given, the area of the circle is 154 sq cm. Therefore, we substitute the value of area to find the radius of the circle.

Area of the circle $=\pi r^2\Rightarrow 154=\frac{22}{7}{r}^2$
$r^2=\frac{154\times 7}{22}\Rightarrow r^2=49\Rightarrow r=7$ cm

Thus, the radius of the circle is $7$ cm.

Given, the radius of the sphere is the same as that of the circle. Thus, the sphere can be represented as:


The volume of the sphere can be calculated as follows:

Volume of the sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\left(\frac{22}{7}\right)(7{)}^3=\frac{30184}{21}=1437.33$ cu cm
Hence, the volume of the sphere is $1437.33$ cu cm.