Question

If the circumference of the base of a hemisphere is $2\pi $ then its volume is ______$cm^3$.
$
  {\text{A}}{\text{. }}\dfrac{{2\pi }}{3}{r^3} \\
  {\text{B}}{\text{. }}\dfrac{{2\pi }}{3} \\
  {\text{C}}{\text{. }}\dfrac{{8\pi }}{3} \\
  {\text{D}}{\text{. }}\dfrac{\pi }{{12}} \\
$

Answer 1

Hint: In this question we need to find the volume of a hemisphere. In order to solve this question, we will use the formula of circumference of a circle and also the formula for volume of hemisphere.

Complete step-by-step answer:
We have been given that the circumference of the base of a hemisphere is $2\pi $ and as we know that the base of a hemisphere is a circle. Hence, it’s circumference will be equal to $2\pi r$.

$ \Rightarrow 2\pi = 2\pi r$

$ \Rightarrow r = 1$

So, the radius of the given hemisphere is 1cm.

Now as we know that the volume of a hemisphere $ = \dfrac{{2\pi }}{3}{r^3}$

Using this formula, we get,

${\text{Volume of Hemisphere}} = \dfrac{{2\pi }}{3}{1^3}$

$ \Rightarrow {\text{Volume of Hemisphere}} = \dfrac{{2\pi }}{3}$

Hence, option B. is correct.

Note: Whenever we face such types of problems the main point to remember is that we need to have a good grasp over mensuration and its formulas. In these types of questions, we should always firstly find the radius and then proceed. This helps in getting us the required condition and gets us on the right track to reach the answer.