Question

A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.

net drawing of a cylinder is shown as two circles with diameters labeled 17 inches and a rectangle with a height labeled 5 inches

How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.

2,081.82 square inches
1,174.36 square inches
720.63 square inches
493.77 square inches

Answer 1

720.33 square inches.

Explanation:

To find the amount of leather needed to create the travel case, you need to find the surface area of the cylinder. The surface area of a cylinder is given by the formula:

SA=2πr2+2πrh

where r is the radius of the base and h is the height of the cylinder. In this case, the radius is half of the diameter, so r = 17/2 = 8.5 inches. The height is given as 5 inches. Using π = 3.14, we can plug in these values and get:

SA=2×3.14×8.52+2×3.14×8.5×5

SA=452.38+267.95

SA=720.33

Therefore, the amount of leather needed is approximately 720.33 square inches. The closest answer is C. 720.63 square inches.

Answer 2

720.63 square inches

To find the surface area of the cylindrical travel case, we need to add the areas of the two circular bases and the lateral surface area.

The diameter of the circular bases is given as 17 inches, so the radius is 17/2 = 8.5 inches. Using the formula for the area of a circle, we can find the area of one base:

Area of one base = πr^2 = 3.14 x 8.5^2 = 226.96 square inches

Since there are two circular bases, the total area of both bases is:

Total area of both bases = 2 x 226.96 = 453.92 square inches

The lateral surface area is a rectangle with height 5 inches and length equal to the circumference of the circular base. We can find the circumference using the formula:

Circumference = 2πr = 2 x 3.14 x 8.5 = 53.38 inches

So, the lateral surface area is:

Lateral surface area = height x circumference = 5 x 53.38 = 266.9 square inches

Therefore, the total surface area of the cylindrical travel case is:

Total surface area = 453.92 + 266.9 = 720.82 square inches (rounded to two decimal places)

So, the answer is approximately 720.63 square inches (rounded to two decimal places).