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If the volume of a sphere is increasing ...

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is

A

a constant

B

proportional to the radius

C

inversely proportional to the radius

D

inversely proportional to the surface area

Text Solution

Verified by Experts

The correct Answer is:
D
Given `(dV)/(dt)=k` [say]
`V=4/3pir^(3)=(dV)/(dt)=4pir^(2)(dr)/(dt)`
`:.(dr)/(dt)=k/(4pir^(2))`
`implies` Rate of increasing radius is inversely proportional to surface area.
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