# The volume of a sphere is given bby the equation V = frac{1}{6sqrt{pi}} S^{3/2}, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meter. Use 3.14 for pi.

The volume of a sphere is given bby the equation $$\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{\frac{{3}}{{2}}}}$$, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meter. Use 3.14 for $$\displaystyle\pi$$.

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Given:
The surface area of the sphere is $$\displaystyle{S}\ =\ {60}{m}^{{{2}}}$$
Concept used:
Volume of the sphere whose surface area is S is given by:
$$\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{{\frac{{{3}}}{{{2}}}}}}$$
Calculation:
The volume of the sphere is:
$$\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{{\frac{{{3}}}{{{2}}}}}}$$
$$\displaystyle={\frac{{{1}}}{{{6}\sqrt{{{3.14}}}}}}{\left({60}\right)}^{{{\frac{{{3}}}{{{2}}}}}}$$
$$\displaystyle\approx{\frac{{{1}}}{{{6}{\left({1.772}\right)}}}}{\left[{7.74597}\right]}^{{{3}}}$$
$$\displaystyle\approx{\frac{{{1}}}{{{10.632}}}}{\left({464.7586}\right)}$$
$$\displaystyle\approx{43.71}$$
The volume of the sphere (to the nearest cubic meter) is about $$\displaystyle{44}{m}^{{{3}}}$$