Answer
Let the side and the volume of a cube be $a=a(t)$ and $V=(t)$ respectively. where $a$ and $V$ are functions of time.
The problem can be restated as follows:
Find $\dfrac{dV}{dt}$, if $\dfrac{da}{dt}=0.5$ cm/s. Where $a$ and $V$ are function of changing side and changing volume of a cube.
Work Step by Step
Let the side and the volume of a cube be $a=a(t)$ and $V=(t)$ respectively. where $a$ and $V$ are functions of time.
Since side is increasing at a rate of $0.5$ cm/s.
$\dfrac{da}{dt}=0.5$ cm/s
And the volume is also increasing at an unknown rate.
That can be written as $\dfrac{dV}{dt}$.
Thus the problem can be restated as follows:
Find $\dfrac{dV}{dt}$, if $\dfrac{da}{dt}=0.5$ cm/s. Where $a$ and $V$ are function of changing side and changing volume of a cube.
