Question

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

Answer 1

Hint: The volume of the hemisphere is given by $\dfrac{{2\pi }}{3}{r^3}$ , where ‘$r$’ is the radius of the hemisphere. Circumference of the hemisphere is given by $2\pi r$, where ‘$r$’ is the radius of the hemisphere. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:

Given the circumference of base of a hemisphere is $2\pi$
But circumference of the hemisphere is given by $2\pi r$
By comparing the above data, we have

$$\Rightarrow 2\pi r = 2\pi \\\ \therefore r = 1cm \\\$$

So, the radius of the hemisphere is 1 cm.
Now, volume of the sphere is given by $V = \dfrac{{2\pi }}{3}{r^3}$

$$\Rightarrow V = \dfrac{{2\pi }}{3}{\left( 1 \right)^3} \\\ \Rightarrow V = \dfrac{{2\pi }}{3} \times 1 \\\ \therefore V = \dfrac{{2\pi }}{3}c{m^3} \\\$$

Thus, the correct option is B. $\dfrac{{2\pi }}{3}$

Note: In math, a hemisphere is defined as a three-dimensional shape that’s half of a sphere with one flat, circular side. Always mention the units after writing the answer. Here the units of volume is $c{m^3}$.