Answer to Question #332079 in Calculus for LM.

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?

[8]

Answer 1

$V=a^3.$

$\frac{dV}{dt}=3a^2\frac{da}{dt}.$

$\frac{da}{dt}=\frac{1}{3a^2}\frac{dV}{dt}=\frac{1200}{3*20^2}=1\frac{cm}{min}.$