If a sphere is inscribed in a cube, then find the ratio of the volume of sphere to the volume of the cube.

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Solution

$\begin{matrix} I f s i d e s o f c u b e b e a c u t e t h e n, \frac{v o l u m e o f s p h e r e}{v o l u m e o f c u b e} = \frac{\frac{4}{3} π \frac{a^{3}}{8}}{a^{3}} \frac{v o l u m e o f s p h e r e}{v o l u m e o f c u b e} = \frac{π}{6} = π : 6 \end{matrix}$

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If a sphere is inscribed in a cube, then find the ratio of the volume of sphere to the volume of the cube.

Ifsidesofcubebeacutethen,volumeofspherevolumeofcube=43πa38a3volumeofspherevolumeofcube=π6=π:6

$\begin{matrix} I f s i d e s o f c u b e b e a c u t e t h e n, \frac{v o l u m e o f s p h e r e}{v o l u m e o f c u b e} = \frac{\frac{4}{3} π \frac{a^{3}}{8}}{a^{3}} \frac{v o l u m e o f s p h e r e}{v o l u m e o f c u b e} = \frac{π}{6} = π : 6 \end{matrix}$