Question

If the edge of a cube is increasing at the rate of $5cm/s$, find the rate of increasing of its volume when its edge is $8cm$ long?

Answer 1

Suppose edge of cube $=a,$ Time $=t,$ Volume $=V$
$\therefore V=a^3$
According to question, at time $t$ increase in rate edge of cube
$\frac{da}{dt}=5cm/s$.
$\therefore$ at time $t$ increase in rate volume
$=\frac{dV}{dt}$
$=\frac{d}{dt}{a}^3$
$=\frac{d}{da}{a}^3.\frac{da}{dt}$
$=3a^2\times 5$
$=15a^2$
When $a=8cm$
Increase in rate of Volume of the cube
$=15(8{)}^2$
$=15\times 64$
$=960c{m}^3/s$.