Exercise 4 Page 593

We are given that an unused roll of paper is in the shape of the following figure.

Note that the figure is a cylinder with a cylindrical hole. To find the volume of the figure, we need to find the volume of each cylinder and subtract the volume of the smaller cylinder from the volume of the larger cylinder. We will start with the larger cylinder. Recall that the volume of a cylinder with the radius $r$ and height $h$ can be calculated by the following formula. In the case of the larger cylinder, we are given the diameter and the height. To find the radius we can divide the diameter $d$ by $2.$ We got that the radius of the larger cylinder is $7$ centimeters. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder. The volume of the larger cylinder is about $4310{\text{ cm}}^3.$ Next, we will find the volume of the smaller cylinder. In this case, we are also given the diameter and the height of the cylinder. To find the radius we can divide the diameter by $2.$ We got that the radius of the smaller cylinder is $2.25$ centimeters. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder. The volume of the smaller cylinder is about $445{\text{ cm}}^3.$ Finally, we can calculate the volume of the roll of paper towels by subtracting the volume of the smaller cylinder from the volume of the larger cylinder. Therefore, the volume of the roll of paper towels is about $3865{\text{ cm}}^3.$