Simone has a red cylindrical storage box that she would like to decorate with patterned paper. The radius of the box is 4.5 inches and the height is 10.2 inches. The cylinder’s net is shown below. How much paper will Simone need to cover the entire box? (Use 3.14 for π.)(1 point)Responses 74.16 square inches 74.16 square inches 206.55 square inches 206.55 square inches 415.42 square inches 415.42 square inches 648.57 square inches

Answer 1

To find the total surface area of the cylinder, we need to find the lateral surface area and the area of the two circular bases.

First, let's find the lateral surface area:
Lateral surface area = 2πrh
Lateral surface area = 2(3.14)(4.5)(10.2)
Lateral surface area = 289.08 square inches

Next, let's find the area of the two circular bases:
Circular base area = πr^2
Circular base area = 3.14(4.5)^2
Circular base area = 63.585 square inches

Now, to find the total surface area, we add the lateral surface area and the area of the two circular bases:
Total surface area = 289.08 + 63.585 + 63.585
Total surface area = 416.25 square inches

Therefore, Simone will need 416.25 square inches of patterned paper to cover the entire box.

The closest option provided is 415.42 square inches.