We are given a mail tube that is in the shape of the following cylinder.
We are asked to estimate what percent of the surface area of the mail tube is cardboard. Note that the area of the cardboard used to make the tube is equal to the lateral area of the tube. Therefore, we need to find the the surface area and the lateral area of the tube. Let's start with the surface area. To calculate the surface area of a cylinder, we can use the following formula.
S=2π rh+2π r^2In this formula, r is the radius of the base and h is the height of the cylinder. We can see that the mail tube has a radius of 2.5 inches and a height of 15 inches. Therefore, we can substitute the radius and the height into the formula. Then we will simplify the right-hand side to get the surface area of the tube. Let's do it!
We got that the surface area of the mail tube is about 274.9 square inches. Next, we will find the lateral area of the mail tube. To do so, we will use the following formula.
L.A.=2π rh
Let's substitute the height and the radius of the mail tube into the formula and calculate the lateral area.
The lateral area of the tube is about 235.6 square inches. This means that the area of the cardboard used to make the tube is also about 235.6 square inches. Finally, we can find the percentage by dividing the area of the cardboard by the surface area.
