Question

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

Answer 1

diameter of sphere = edge of cube
let radius of sphere be x units
therefore edge of cube = 2x units
volume of cube = a³
= (2x)³ = 8x³
volume of sphere = 4/3 π r³
$= \frac{4}{3} \times \frac{22}{7} \times {x}^{3} \\ = \frac{88 {x}^{3} }{21}$
therefore
$\frac{vol(cube)}{vol(sphere)} = \frac{8 {x}^{3} }{ \frac{88 {x}^{3} }{21} } \times \frac{21}{21} = \frac{168 {x}^{3} }{88 {x}^{3} } \\ = \frac{21}{11}$
therefore the ratio of cube's volume to sphere's volume is 21:11

Answer 2

hey mate !!❤✌
here's ur answer ✍✍✍

➡️Refer to attachment

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