Question

If the volume of a cube increases at rate of 3 cm^3/sec what is the rate of increase of the length of its side ?

Answer 1

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We know that

V = L³ ⇒ L = ∛V

and

dV/dt = 3cm³/s (volume rate as a function of time)

Let

dL/dV = L' = 1/(3∛V²)

We need dL/dt (side rate as a function of time), so

(dV/dt) . (dL/dV) = dL/dt

then

dL/dt = 3 . [1/(3∛V²)]

dL/dt = 1/∛V²