A company wants to manufacture rolls of toilet paper. The toilet paper roll is in the shape of a hollow cylinder with a diameter of 4.75 inches. The thickness of the paper is 1.7 inches. The height of the toilet paper roll is 3.9 inches. The toilet paper costs $.02 per cubic inch. How much will it cost to manufacture 50 rolls of toilet paper?

$ 40.6 to make the 50 rolls of toilet paper

Step-by-step explanation:

We have that the diameter of every cylinder is 4.75 inches, therefore the gap would be that value minus the thickness of the paper, like this:

4.75 - 1.7 = 3.05

3.05 inches would be the diameter of the hole.

Now, to know the volume of the paper, we would have to calculate the total volume and then subtract the volume of the hole.

First we calculate the radii:

r = d / 2

r1 = 4.75 / 2

r1 = 2.375 in

r2 = 3.05 / 2

r2 = 1.525 in

Now if we calculate the volumes

Total volume:

Vt = pi * (r ^ 2) * h

Vt = 3.14 * (2,375 ^ 2) * 3.9

Vt = 69.08 in ^ 3

Hollow volume

Vh = 3.14 * (1,525 ^ 2) * 3.9

Vh = 28.48 in ^ 3

We subtract:

Vt - Vh = 69.08- 28.48 = 40.6

40.6 in ^ 3 would be the volume of the toilet paper

We need to know what it costs to create 50, we know it costs $ 0.02 per cubic inch

Then it would be:

40.6 * 0.02 = 0.812

In other words, making one costs $ 0.812, so making 50 would cost:

0.812 * 50 = 40.6

In other words, it costs $ 40.6 to make the 50 rolls of toilet paper