Question

The volume of a solid hemisphere is $1152\pi c{m}^3$. Find its curved surface area.

Answer 1

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

It is given that the volume of hemisphere is$V=1152\pi$ cm${}^3$ and thus,

$V=\frac{2}{3}\pi r^3\Rightarrow 1152\pi =\frac{2}{3}\pi r^3\Rightarrow r^3=\frac{1152\times 3}{2}=1728\Rightarrow r=\sqrt[3]{31728}=12$

Therefore, the radius of hemisphere is $12$ cm.

We also know that the curved surface area of hemisphere with radius $r$ is $A=2\pi r^2$.

Here, the radius of hemisphere is $12$ cm, thus,

$A=2\pi r^2=2\times \frac{22}{7}\times (12{)}^2=2\times \frac{22}{7}\times 144=905.14$cm${}^2$

Hence, the curved surface area of hemisphere is $905.14$ cm${}^2$.