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Q.
An edge of a variable cube is increasing at the rate of $10\, cm / s$. How fast the volume of the cube will increase when the edge is $5 \,cm$ long?
Application of Derivatives
Solution:
Let $l$ be the length of an edge and $V$ be the volume of cube at any timet.
$\because V =l^3$
$\therefore \frac{d V}{d t} =3 l^2 \frac{d l}{d t}$
$=3 \times 5^2 \times 10 \,cm ^3 / s$
$ =750 \,cm ^3 / s$