Question

Find the radius of hemisphere of total surface ate 4158 sqcm

Answer 1

TSA=3πr^2=4158

r^2=4158/{3*3.14}=441.4012

r=√441.4=21.0095

Therefore the radius is 21.01cm approximately

Answer 2

Given,

The total surface area of hemisphere is 4158.

To find out,

The radius of the hemisphere.

Solution:

$\huge \: total \: surface \: area \: of \: hemisphere \: = 3 \pi \: {r}^{2} \\ \\ 4158 = 3 \times \frac{22}{7} \times {r}^{2} \\ \\ \frac{4158}{3} = \frac{22}{7} \times {r}^{2} \\ \\ 1386 = \frac{22}{7} = {r}^{2} \\ \\ \frac{1386 \times 7}{22} = {r}^{2} \\ \\ \frac{9702}{22} = {r}^{2} \\ \\ 441 = {r}^{2} \\ \\ r \: = \sqrt{441} \\ \\ r = 21cm$

Therefore the radius of the hemisphere is 21 cm.

Proof:

$total \: surface \: area \: of \: hemisphere \: = 3 \pi \: {r}^{2} \\ \\ 4158 = 3 \times \frac{22}{7} \times 21 \times 21 \\ \\ \frac{4158}{3} = \frac{22 \times 21 \times 21}{7} \\ \\ 1386 = \frac{9702}{7} \\ \\ 1386 = 1386$