Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 3 in. long and increasing at the rate of 0.2 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?

DV (t) = 5.4 in³/s

Step-by-step explanation:

Volume of cube of side x is Vc = x³

If the sides are increasing at a rate 0.2 in/sec and sides of a cube are 3 in.

V (t) = x³

Taking derivatives on both sides of the equation we get

DV (t) = 3*x² * dx/dt (2)

Plugging values in equation (2)

DV (t) = 3 * (3) ² * 0,2 ⇒ DV (t) = 5.4 in³/s