Question

The edge of a cube is increasing at a rate of 7 cm/s. Find the rate of change of area of the cube when x=6 cm.

(a) 578 cm^2/s

(b) 498 cm^2/s

(c) 504 cm^2/s

(d) 688 cm^2/s

I had been asked this question in unit test.

The doubt is from Derivatives Application topic in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (c) 504 cm^2/s

The explanation: Let the edge of the cube be x. The rate of change of edge of the cube is given by \(\frac{dx}{dt}\)=7cm/s.

The area of the cube is A=6x^2

∴\(\frac{dA}{dt}=\frac{d}{dt} \)(6x^2)=12x.\(\frac{dx}{dt}\)=12x×7=84x

\(\frac{dA}{dt}\)|_x=6=84×6=504 cm^2/s.