Question

The volume of the hemisphere is 2425. Find its curved surface are?

Answer 1

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Answer 2

Given,

The volume of the hemisphere = 2425

To find out,

The curved surface area of hemisphere.

Solution:

$\huge \: volume \: of \: hemisphere = \frac{2}{3} \pi \: {r}^{3} \\ 2425 = \frac{2}{3} \times \frac{22}{7} \times {r}^{3} \\ \\ 2425 = \frac{44}{21} \times {r}^{3} \\ \\ \frac{2425 \times 21}{44} = {r}^{3} \\ \\ \frac{50925}{44} = {r}^{3} \\ \\ 1157.38 = {r}^{3} \\ \\ r = \sqrt[3]{157.38} \\ \\ r = 10.49926$

Now,

$\huge \: curved \: surface \: area \: of \: hemisphere(csa) = 2 \pi \: {r}^{2} \\ \\ csa \: of \: hemisphere \: = 2 \times \frac{22}{7} \times 10.49926 \times 10.49926 \\ \\ csa \: of \: hemisphere \: = \frac{44}{7} \times 110.2344 \\ \\ csa \: of \: hemisphere \: = \frac{4850.3136}{7} \\ \\ csa \: of \: hemisphere \: = 692.90 \: square \: units$

Therefore the curved surface area of hemisphere is 692.90 square units.