Question

If the volume of a hemisphere is 19404 cm", then the total surface area of the
hemisphere is :
​

Answer 1

Answer:

.

.

.

.

.

.

=4158  cm  

Answer 2

• Total surface area of hemisphere is 87310.57 cm² (approximately)

Step-by-step explanation:

Given:-

• Volume of hemisphere is 19404 cm³.

To find:-

• Total surface area of hemisphere.

Solution:-

• First we need Radius for Total surface area of hemisphere.

We know that,

$\boxed{\star \: \bold{Volume \: of\: hemisphere = \cfrac{2}{3} \pi r^{2}}}$

In which,

• r is Radius of hemisphere.

Volume of hemisphere = 19404 cm³

Put Volume of hemisphere in form:

$\longrightarrow \sf \bold{19404 = \cfrac{2}{3} \times \cfrac{22}{7} \times {r}^{2} }$

$\longrightarrow \sf \bold{ \cfrac{19404 \times 3}{2} = \cfrac{22}{7} \times {r}^{2} }$

$\longrightarrow \sf \bold{9702 \times 3 = \cfrac{22}{7} \times {r}^{2} }$

$\longrightarrow \sf \bold{ \cfrac{9702 \times 3 \times 7}{22} = {r}^{2} }$

$\longrightarrow \sf \bold{ \cfrac{203742}{22} = {r}^{2} }$

$\longrightarrow \sf \bold{9261 = {r}^{2} }$

$\longrightarrow \sf \bold{ \sqrt{9261} = r}$

$\longrightarrow \sf \bold{96.23 = r}$

Or, r = 96.23

So, Radius of hemisphere is 96.23 (approx.)

$\boxed{\star \: \bold{Total \: surface\:area = 3 \pi r^{2}}}$

$\longrightarrow \sf \bold{3 \times \cfrac{22}{7} \times 96.23 \times 96.23}$

$\longrightarrow \sf \bold{ \cfrac{611174.051}{7} }$

$\longrightarrow \sf \bold{87310.57}$

Therefore,

Total surface area of hemisphere is 87310.57 cm² (approximately).