Question

If the circumference of base of a hemisphere is $2\mathrm{\pi }$. Then what will be its volume

Answer 1

Step 1: Find the radius of given hemisphere

Given that the circumference of the base is $2\mathrm{\pi }$

Let $r$ be the radius of the hemisphere

$$\begin{gathered} \mathrm{Circumference}=2\mathrm{\pi r} \\ \Rightarrow 2\mathrm{\pi }=2\mathrm{\pi r} \\ \Rightarrow \mathrm{r}=1unit \end{gathered}$$

Therefore the radius of the hemisphere is $1\mathrm{unit}$

Step 2: Find the Volume

We know that the volume of a hemisphere with radius $r$ is $\frac{2}{3}{\mathrm{\pi r}}^3$

$$\begin{gathered} \mathrm{Volume}=\frac{2}{3}·\mathrm{\pi }·{\mathrm{r}}^3 \\ \Rightarrow \mathrm{Volume}=\frac{2}{3}·\mathrm{\pi }·{\left(1\right)}^3 \\ \Rightarrow \mathrm{Volume}=\frac{2}{3}·\mathrm{\pi } \end{gathered}$$

Therefore the volume is $\frac{2}{3}\mathrm{\pi }{\mathrm{unit}}^3$

Hence, volume of the hemisphere is $\frac{2}{3}\mathrm{\pi }{\mathrm{unit}}^3$