Question

If the area of a circle is increasing at a uniform rate, prove that rate of increasing of perimeter is inversely proportional to its radius.


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Answer 1

HERE IS YOUR ANSWER.

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STEP 1.

Area of circle = πr^2

Differentiating w.r.t t on both sides we get,

dA/dt = π2r. dr/dt

It is given that the area is increasing at uniform rate

therefore ,

dA/dt = K ➡2 πr (dr/dt) =K

STEP 2.

Where K is constant

therefore ,

dr/dt = K/2π r

Perimeter of the circle is

p=2πr

Differentiatily w.r.t t we get

dpdt=2π.drdt

Substituting for drdt we get

dpdt=2π.k2πr

dpdt=kr

⇒dpdt α 1r

Hence this proves that the perimeter varies inversely as the radius.

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HOPE IT HELPS YOU! ! !

Answer 2

Solution:-

Refer to the Attachment!!

Hence,

We Conclude that the Rate of Increase of the Perimeter varies Inversely to Radius.

Hope it Helps!!