A metal cube expands as it is heated

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A metal cube expands as it is heated. When the edge length is

3\,\text{cm}

, the volume is increasing at

225\,\text{cm}^{3}/\text{min}

. At that instant, how fast is the cube’s surface area increasing? (a)

450\,\text{cm}^{2}/\text{min}

(b)

300\,\text{cm}^{2}/\text{min}

(c)

900\,\text{cm}^{2}/\text{min}

(d)

75\,\text{cm}^{2}/\text{min}