Question

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?

Answer 1

Solution;

$\frac{dV}{dt}=1200cm^3/min$

x=20cm

But;

$V=x^3$

Differentiate with respect to time,t;

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

Where;

$\frac{dx}{dt}$ is the increasing rate of one side.

Back substitution;

$200=3(20^2)\frac{dx}{dt}$

Hence;

$\frac{dx}{dt}=1.667cm/min$