Find the rate of change of volume of the cube when the side of the cube is 10 cm. It is known that the side changes at the rate of 4 cm/s.

Concept:

The rate of change of the value of a function f(x) with respect to a variable t, is given by: \(\rm \frac {df(x)}{dt}\)

Calculation:

Given the side of the cube L = 10cm and \(\rm dL\over dt\) = 4 cm/s

Now volume of the cube V = L3 

\(\rm dV\over dt\) = \(\rm dV\over dL\) × \(\rm dL\over dt\)

\(\rm dV\over dt\) = \(\rm dL^3\over dL\) × 4

\(\rm dV\over dt\) = 3L2 × 4

\(\rm dV\over dt\) = 12 × 102 

\(\rm dV\over dt\) = 1200 cm3/s