Question

Find the volume of a hemisphere whose radius is 7 cm. $(\text{use }\pi ={\displaystyle \frac{22}{7}})$
A) 112.66 $c{m}^3$
B) 718.66 $c{m}^3$
C) 12.66 $c{m}^3$
D) 132.66 $c{m}^3$

Answer 1

Hint: To specify a figure most fundamental quantities are perimeter, area and volume. Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object. We have a predefined formula for evaluating volume of hemisphere. So, using this formula we can easily solve our problem.

Complete step-by-step answer:

For our problem, we have a hemisphere whose radius is given. It can be assumed as a bowl having some definite radius.
So, the volume of the hemisphere can be specified by the cubic product of radius with some constant.
This can be represented in mathematical expression as: $V={\displaystyle \frac{2}{3}}\pi r^3$, where r be the radius of the hemisphere with some other constant values.

The hemisphere has a radius of 7 cm. The cube of radius is 343 $c{m}^3$.
So, the volume will be:
$$\begin{array}{rl}& ={\displaystyle \frac{2}{3}}\times {\displaystyle \frac{22}{7}}\times 7\times 7\times 7\\ & ={\displaystyle \frac{2156}{3}}\\ & =718.66c{m}^3\end{array}$$
Therefore, the volume of the hemisphere of radius 7 cm is 718.66 cubic cm.
Hence, option (b) is correct.

Note: The key step for solving this problem is the knowledge of volume of a hemisphere. By using the suitable formula, the volume of hemisphere is evaluated without any error. This knowledge is useful in solving complex problems related to volume of a figure.