Question

A cube has an edge of 5 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.

Answer 1

INFORMATION:

We know that:

- A cube has an edge of 5 feet

- The edge is increasing at the rate of 2 feet per minute

And we must express the volume of the cube as a function of m, the number of minutes elapsed

STEP BY STEP EXPLANATION:

First, we need to use that the volume of a cube of edge e is given by:

$V=e^3$

Second, we can find an expression for the variation of the edge in terms of the time. The edge starts at 5 feet, and increases at the rate of 2 feet per minute

$e(m)=5+2m$

Finally, replacing the function for the edge variation in the formula for the volume of a cube

$V(m)=(5+2m)^3$

ANSWER:

The expression for the volume of the cube as a function of m is:

$V(m)=(5+2m)^3$