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If the rate of change of area of a circl...

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to

A

`(2)/(pi)` unit

B

`(1)/(pi)` unit

C

`(pi)/(2)` units

D

`pi` units

Text Solution

Verified by Experts

The correct Answer is:
A
Let x be the diameter and A be the area of a circle.
Then,
`A=(pi)/(4)x^(2)`
`implies (dA)/(dt)=(pi)/(2)x(dx)/(dt)`
`implies(dx)/(dt)=(pix)/(2)(dx)/(dt)" "[because(dA)/(dt)=(dx)/(dt)"(given)"]`
`implies x=(2)/(pi)`
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