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Find the rate of change of the volume of...

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

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The correct Answer is:
1
`V=4/3pir^(3),S=4pir^(2)`
`(dV)/(dr)=4pir^(2),(dS)/(dr)=8pir^(2)`
`implies(dV)/(ds)=(dV//dr)/(dS//dr)=r/2`
when `r=2`
`(dr)/(dS)=1`
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