$\begin{array}{1 1} (A)\;900cm^3/s \\ (B)\;500cm^3/s \\ (C)\;600cm^3/s \\(D)\;100cm^3/s \end{array} $

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- If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
- $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$

Step 1:

Given : $\large\frac{da}{dt}$$=3cm/s$ and $a=10cm$

Volume of the cube =$a^3$

Differentiating w.r.t $t$ on both sides we get,

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

Step 2:

Substituting for $a$ and $\large\frac{da}{dt}$

$\large\frac{dv}{dt}$$=3\times 10\times 10\times 3$

$\quad=900cm^3/s$

The rate at which the volume of the cube when the edge is $900cm^3/s$

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