An edge of a variable cube is increasing at the rate of 10cm. How fast the volume of the cube will increase when the edge is 5cm long?

Question

An edge of a variable cube is increasing at the rate of 10 $\mathrm{cm} / \mathrm{s}$. How fast the volume of the cube will increase when the edge is $5 \mathrm{~cm}$ long?

(a) $750 \mathrm{~cm}^3 / \mathrm{s}$

(b) $75 \mathrm{~cm}^3 / \mathrm{s}$

(c) $300 \mathrm{~cm}^3 / \mathrm{s}$

(d) $150 \mathrm{~cm}^3 / \mathrm{s}$

Answer 1

SOLUTION — Let $l$ be the length of an edge

$\therefore V  =l^3 \\$

$\Rightarrow  \frac{d V}{d t}  =3 l^2 \frac{d l}{d t}=3 \times 5^2 \times 10 \\$

$=750 \mathrm{~cm}^3 / \mathrm{s}$

So, The correct option of this question will be (A).