If the radius of a circle changes at the rate of {-2}/\pi m/s at what rate does the circle's area change when the radius is 10 m?

Correct Answer is : - 40 m2∕s

NIMCET 2018 Question Paper with solutions

Question : 50 of 120

Marks: +1, -0

If the radius of a circle changes at the rate of

{-2}/π

m/s at what rate does the circle's area change when the radius is 10 m?

Solution:

Given that ,

{dr}/{dt}

{-2}/π

m/s
We know that,
Area of circle =

πr^2

∴ A =

πr^2

Differentiate w.r.t to t, we get

{dA}/{dt}

= π (2r) .

{dr}/{dt}

= 2πr

(-2/π)m^2\/s

= -

{4π}/π

(10)

m^2

/s [given , r = 10]
= - 40

m^2

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