Question

The volume of a cube of edge x is increasing at a rate of 12 cm/s. Find the rate of change of edge of the cube when the edge is 6 cm.

(a) \(\frac{1}{8}\)

(b) \(\frac{2}{9}\)

(c) –\(\frac{1}{9}\)

(d) \(\frac{1}{9}\)

The question was asked by my school principal while I was bunking the class.

The question is from Derivatives Application topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (d) \(\frac{1}{9}\)

Explanation: Let the volume of cube be V.

V=x^3

\(\frac{dV}{dt}\)=3x^2 \(\frac{dx}{dt}\)

12=3x^2 \(\frac{dx}{dt}\)

\(\frac{dx}{dt}=\frac{4}{x^2}\)

\(\frac{dx}{dt}\)|_x=6=\(\frac{4}{6^2}=\frac{4}{36}=\frac{1}{9}\).