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