Question

Volume of a hemisphere is 144 pi cubic cm. Find the CSA and TSA.

Answer 1

Hello friends!! Nice question..

Here is ur answer :

First, the formula used in this question :

Volume of hemisphere

$\frac{2}{3} \pi {r}^{3}$


Curved surface area of hemisphere

$= 2\pi {r}^{2}$



Total surface area of hemisphere

$= 3\pi {r}^{2}$


Now come to the question,

Volume of hemisphere
$= 144\pi \: \: {cm}^{3}$


We have to find radius of hemisphere.

Let the radius be r.

According to question,

$\frac{2}{3} \pi {r}^{3} = 144\pi$


$\pi \: \: cancel \: \: out$


$\frac{2}{3} {r}^{3} = 144$


${r}^{3} = 144 \times \frac{3}{2}$


${r}^{3} = 72 \times 3$


${r}^{3} = 216$


$r = \sqrt[3]{216}$


$r = 6 \: \: cm$



Now find,

Curved surface area of hemisphere

$= 2 \times \pi \times {(6)}^{2}$


$= 2 \times \pi \times 36$

$= 72\pi \: \: {cm}^{2}$


________________

Total surface area of hemisphere


$= 3 \times \pi \times {(6)}^{2}$

$= 3 \times \pi \times 36$

$= 108\pi \: \: {cm}^{2}$



HOPE IT HELPS YOU..