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.)

Question

(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

Answer 1

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

Lateral surface area = 2πrh
Lateral surface area = 2 * 3.14 * 4.5 * 10.2
Lateral surface area = 288.36 square inches

Area of one circular base = πr^2
Area of one circular base = 3.14 * 4.5^2
Area of one circular base = 3.14 * 20.25
Area of one circular base = 63.585 square inches

Total surface area = Lateral surface area + 2 * Area of one circular base
Total surface area = 288.36 + 2 * 63.585
Total surface area = 288.36 + 127.17
Total surface area = 415.53 square inches

Therefore, Simone will need 415.53 square inches of patterned paper to cover the entire box. So, the closest option is 415.42 square inches.