Question

If the circumference of the circle is changing at the rate of 5 cm/s then what will be rate of change of area of the circle if the radius is 6cm.

(a) 20 cm^2/s

(b) 40 cm^2/s

(c) 70 cm^2/s

(d) 30 cm^2/s

The question was posed to me in an international level competition.

The origin of the question is Derivatives Application in division Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (d) 30 cm^2/s

Explanation: The circumference of the circle is given by C=2πr, where r is the radius of the circle.

∴\(\frac{dC}{dt}\)=2π.\(\frac{dr}{dt}\)=5 cm/s

\(\frac{dr}{dt}\)=5/2π cm/s

\(\frac{dA}{dt}\)|r=6=2πr.\(\frac{dr}{dt}\)=2πr.\(\frac{5}{2 \pi}\)=5r=5(6)=30 cm^2/s.