Question

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 4 in. long and increasing at the rate of 0.5 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?

Answer 1

24 in³ per sec.

Explanation:

Since, the volume of a cube ,

`V = x^3-----(1)`

Where,

x = side length,

Differentiating equation (1) w. r. t ( time ),

`(dV)/(dt)=3x^2 (dx)/(dt)`

Here,

`x = 4\text{ in},(dx)/(dt)= 0.5\text{ in per sec}`

`\implies (dV)/(dt)=3(4)^2(0.5) = 24\text{ cube in per sec}`

That is, volume of the cube is changing with the rate of 24 in³ per sec.