If surface area and volume of a sphere are S | vedclass

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Question

(A) The surface area $S$ of a sphere with radius $r$ is given by $S = 4 \pi r^{2}$.The volume $V$ of a sphere with radius $r$ is given by $V = \frac{4

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(A) The surface area $S$ of a sphere with radius $r$ is given by $S = 4 \pi r^{2}$.The volume $V$ of a sphere with radius $r$ is given by $V = \frac{4}{3} \pi r^{3}$.We need to calculate the value of $\frac{S^{3}}{V^{2}}$.First,calculate $S^{3} = (4 \pi r^{2})^{3} = 64 \pi^{3} r^{6}$.Next,calculate $V^{2} = (\frac{4}{3} \pi r^{3})^{2} = \frac{16}{9} \pi^{2} r^{6}$.Now,divide $S^{3}$ by $V^{2}$:$\frac{S^{3}}{V^{2}} = \frac{64 \pi^{3} r^{6}}{\frac{16}{9} \pi^{2} r^{6}} = \frac{64 \pi^{3} r^{6} 	imes 9}{16 \pi^{2} r^{6}} = \frac{64 	imes 9}{16} 	imes \frac{\pi^{3}}{\pi^{2}} = 4 	imes 9 	imes \pi = 36 \pi$.Thus,the value is $36 \pi$.

If surface area and volume of a sphere are $S$ and $V$,respectively,then the value of $\frac{S^{3}}{V^{2}}$ is......$\pi$.

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