Question

find surface area of a sphere whose volume is 99 by 7cm

Answer 1

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$\underline{SOLUTION}$ ➡


$Given, \\ \\ Volumn \: \: of \: \: the \: \: sphere \: = \frac{99}{7} \: \: cu \: \: cm$

$Let ,\\ \\ Radius \: \: of \: \: the \: \: sphere \: = r \\ \\ So,\\ \\ Volumn \: \: of \: \: the \: \: sphere \: = \frac{4}{3} \pi \: r {}^{3}$

$Therefore, \\ \\ \frac{4}{3} \pi \: r {}^{9} = \frac{99}{7} \\ \\ = > \frac{4}{3} \times \frac{22}{7} \times r{}^{3} = \frac{99}{7} \\ \\ = > \frac{88}{21} \times r{}^{ 3} = \frac{99}{7} \\ \\ = > r {}^{3} = \frac{99}{7} \times \frac{21}{88} \\ \\ = > r {}^{3} = \frac{27}{8} \\ \\ = > r {}^{3} = ( \frac{3}{2} ) {}^{3} \\ \\ = >r = \frac{3}{2} \\ \\ so \\ \\ radius \: of \: the \: sphere = \frac{3}{2} \: \: cm$

$Surface \: \: of \: \: the \: \: sphere \: = 4\pi \: r {}^{2} \\ \\ = 4 \times \frac{22}{7} \times (\frac{3}{2} ) {}^{2} \: \: sq. \: cm\\ \\ = 4 \times \frac{22}{7} \times \frac{9}{4} \: \: \: sq .\: cm\\ \\ = \frac{198}{7} \: \: sq .\: cm$

$Surface \: \: area \: \: of \: \: the \: \: sphere \: = \frac{198}{7} \: \: sq .\: cm$



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