Question

A cube has an edge of 2.25 feet. The edge is increasing at the rate of 1.25 feet per hour. Express the volume of the cube as a function of h, the number of hours elapsed.

Answer 1

`V(h)=(1.25h+2.25)^3`

Explanation:

Recall that the volume of a cube is given by:

`\displaystyle V = s^3`

Where s is the side length of the cube.

The edges of the cube has an original length of 2.25 feet. It increases by 1.25 feet per hour. In other words, the length s after h hours can be modeled by the equation:

`s=1.25h+2.25`

Substitute. Hence, our function is:

`V(h)=(1.25h+2.25)^3`