Acube has an edge of 5 feet. the edge is increasing at the rate of 4 feet per minute. express the volume of the cube as a function of mm, the number of minutes elapsed.
v(m)=? ?

The function that gives the volume of the cube after m minutes is given by:

The volume of a cube of edge e is given by:

In this problem, the edge is represented by a linear function, which starts at 5 feet, and increases by 4 feet each minute, thus:

Then, the volume is given by:

A similar problem is given at link

Step-by-step explanation:

Given : A cube has an edge of 5 feet. The edge is increasing at the rate of 4 feet per minute.

To Find: Express the volume of the cube as a function of mm, the number of minutes elapsed.

Solution:

We are given that The edge is increasing at the rate of 4 feet per minute.

let x denotes the length of edge

So,

Volume of cube =

Where x is the length of side

Differentiating with respect to time

  --A

Now we are given that A cube has an edge of 5 feet.

So, x= 5

And we are also given that

Substitute the values in A

Now integrating both sides to express the volume of the cube as a function of mm

When m = no. of minutes = 0

So, c = initial volume

Initial volume of cube =

So, the volume of the cube as a function of mm, the number of minutes elapsed is

it would rotate about 180 degrees.