Question

Curved surface area of a hemisphere is $905\frac{1}{7}c{m}^3$, what is its volume?

Answer 1

Given that,

Curved Surface Area of the Hemisphere $=$$905\frac{1}{7}c{m}^3=\frac{6336}{7}c{m}^3$

We know that,

Curved Surface Area (C.S.A) of the Hemisphere $=2{\mathrm{\pi r}}^2$

Therefore,

$$\begin{gathered} 2{\mathrm{\pi r}}^2=\frac{6336}{7} \\ {\mathrm{r}}^2=\frac{6336}{7\times 2\times \mathrm{\pi }} \end{gathered}$$

${\mathrm{r}}^2=\frac{6336}{7\times 2\times {\displaystyle \frac{22}{7}}}$ (Since, $\pi =\frac{22}{7}$)

$$\begin{gathered} r^2=144 \\ r=\sqrt{144} \\ r=12cm \end{gathered}$$

Also,

Volume of the Hemi-sphere $=\frac{2}{3}{\mathrm{\pi r}}^3$

$$\begin{gathered} =\frac{2}{3}\times \frac{22}{7}\times 12\times 12\times 12 \\ =3620.57c{m}^3 \end{gathered}$$

Hence, The volume of the Hemi-sphere is $3620.57c{m}^3$