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A sphere and a cube has same surface are...

A sphere and a cube has same surface area.Show that the ratio of the volume of sphere to cube is `sqrt6:sqrtpi`

Text Solution

Verified by Experts

Surface area of sphere=`4pir^2`
Surface area of circle=6a
According to quastion.
`4pir^2=6a-(1)`
`V_(spher)/V_(cube)=(4/3pir^3)/a^3`
`=4/3pi*(r/a)^3`
`=4/3pisqrt(6/4pi)^3`
`V_(spher)/V_(cube)=sqrt6/sqrtpi`
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