Question

The rate of change of area of a square is 40 cm^2/s. What will be the rate of change of side if the side is 10 cm.

(a) 2 cm/s

(b) 4 cm/s

(c) 8 cm/s

(d) 6 cm/s

I had been asked this question by my college professor while I was bunking the class.

I would like to ask this question from Derivatives Application topic in portion Application of Derivatives of Mathematics – Class 12

Answer 1

The correct answer is (a) 2 cm/s

For explanation: Let the side of the square be x.

A=x^2, where A is the area of the square

Given that, \(\frac{dA}{dt}\)=2x \(\frac{dx}{dt}\)=40 cm^2/s.

\(\frac{dx}{dt}=\frac{20}{x} \)cm/s

\(\frac{dx}{dt}=\frac{20}{10}\)=2 cm/s.