An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long ?

900 $cm^3/s$

The correct answer is Option (3) → 900 $cm^3/s$

Let x → edge

$\frac{dx}{dt}=3cm/s$

Volume = $V(x)=x^3$

$\frac{dV(x)}{dt}=3x^2\frac{dx}{dt}⇒\left.\frac{dV(x)}{dt}\right]_{x=10}=3×10^2×3$

$=900\,cm^3/s$