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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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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?

$\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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1 Answer

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Toolbox:
  • 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 $900cm^3/s$
answered Jul 5, 2013 by sreemathi.v
 

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