Question

If the rate of change of radius of a circle is 6 cm/s then find the rate of change of area of the circle when r=2 cm.

(a) 74.36 cm^2/s

(b) 75.36 cm^2/s

(c) 15.36 cm^2/s

(d) 65.36 cm^2/s

I have been asked this question in quiz.

My doubt stems from Derivatives Application topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (b) 75.36 cm^2/s

To elaborate: The rate of change of radius of the circle is \(\frac{dr}{dt}\)=6 cm/s

The area of a circle is A=πr^2

Differentiating w.r.t t we get,

\(\frac{dA}{dt}=\frac{d}{dt}\) (πr^2)=2πr \(\frac{dr}{dt}\)=2πr(6)=12πr.

\(\frac{dA}{dt}\)|r=2=24π= 24×3.14=75.36 cm^2/s