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The radius of a circular plate increase ...

The radius of a circular plate increase at the rate of `0.1` cm per second. At what rate does the area increase when the radius of plate is `5/pi cm`?

A

`1 cm^(2)//s`

B

`0.1 cm^(2)//s`

C

`0.5 cm^(2)//s`

D

`2 cm^(2)//s`

Text Solution

Verified by Experts

The correct Answer is:
A
Area of disk, `A=pir^(2)` (where r= radius of disk)
`(dA)/(dt)=pi(2r(dr)/(dt))=2pir(dr)/(dt)` so `(dA)/(dt)=2pixx5/pixx0.1=1 cm^(2)//s`
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