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
To find the surface area of the cylindrical storage box, we need to calculate the lateral surface area and the area of the two circular bases separately.
Lateral Surface Area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 286.2 square inches
Area of the two circular bases:
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 area of both circular bases = 2 * 63.585
Total area of both circular bases = 127.17 square inches
Total surface area = Lateral Surface Area + Area of both circular bases
Total surface area = 286.2 + 127.17
Total surface area = 413.37 square inches
Therefore, Simone will need 413.37 square inches of patterned paper to cover the entire box. The closest answer provided is 415.42 square inches.