Question

Volume of a cube is increasing at the rate of $0.003m^2/sec$. At the instant when the edge is $20cm$. Find the rate at which the edge is changing.

Answer 1

Volume of cube = $a^3$

$v=a^3$

$\therefore \frac{dv}{dt}=3a^2\frac{da}{dt}$

$\therefore \frac{3}{1000}=3\times \frac{400}{10000}\times \frac{da}{dt}$

$\therefore \frac{da}{dt}=\frac{1}{40}m/sec$

$\therefore \frac{da}{dt}=0.025m/sec$