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.

fortdefruitI 2021-02-24 Answered
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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Expert Answer

opsadnojD
Answered 2021-02-25 Author has 9920 answers
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:
\(\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{{\frac{{{3}}}{{{2}}}}}}\)
\(\displaystyle={\frac{{{1}}}{{{6}\sqrt{{{3.14}}}}}}{\left({60}\right)}^{{{\frac{{{3}}}{{{2}}}}}}\)
\(\displaystyle\approx{\frac{{{1}}}{{{6}{\left({1.772}\right)}}}}{\left[{7.74597}\right]}^{{{3}}}\)
\(\displaystyle\approx{\frac{{{1}}}{{{10.632}}}}{\left({464.7586}\right)}\)
\(\displaystyle\approx{43.71}\)
Answer:
The volume of the sphere (to the nearest cubic meter) is about \(\displaystyle{44}{m}^{{{3}}}\)
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