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The rate of change of surface area of a ...

The rate of change of surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

A

`(1)/(r^(2))`

B

`(1)/(r )`

C

`r^(2)`

D

r

Text Solution

Verified by Experts

The correct Answer is:
D
Let S be the surface area and r be the radius of the sphere at any time t. Then,
`S=4pi r^(2)`
`implies (dS)/(dt)=8pi r(dr)/(dt)`
`implies (dS)/(dt)=8pirxx2" "[(dr)/(dt)=2cm//sec]`
`implies (dS)/(dt)=16pir implies (dS)/(dt)propr`
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