The edge of a solid cube is increasing uniformly at the rate of

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

0.05\,\text{cm/min}

. Let

x\,(\text{cm})

denote the edge length at time

t\,(\text{min})

. (a) Obtain an expression for the rate of change of the volume of the cube in terms of

x

. (b) Find the rate at which (i) the volume, and (ii) the total surface area are increasing when the edge length is

10\,\text{cm}

. (c) If the volume is increasing at the rate of

15\,\text{cm}^{3}\!\!\text{/min}

, determine the edge length of the cube at that instant.