Class 12 Mathematics - Chapter Application of Derivatives NCERT Solutions | An edge of a variable cube is increasing
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?
Let x be the length of a side and V be the volume of the cube. Then,
V = x3.
\begin{align}\therefore \frac{dV}{dt}=3x^2.\frac{dx}{dt}\;\;\;[By\; Chain \;Rule]\end{align}
It is given that,
\begin{align} \frac{dx}{dt}=3 \;cm^2/s\end{align}
\begin{align}\therefore \frac{dV}{dt}=3x^2.(3) = 9x^2\end{align}
Thus, when x = 10 cm,
\begin{align} \frac{dV}{dt}=9 (10)^2=900 \;cm^3/s\end{align}
Hence, the volume of the cube is increasing at the rate of 900 cm3/s when the edge is 10 cm long.
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1 Comment(s) on this Question
why dv/dt=3x^2.dx/dt
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