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.)
To find the surface area of the cylinder that Simone needs to cover with paper, we need to find the lateral surface area of the cylinder as well as the surface area of the two circular bases.
1. Lateral surface area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 288.036 square inches
2. Surface area of two circular bases:
Surface Area of a circle = πr^2
Surface Area of one base = 3.14 * 4.5^2
Surface Area of one base = 3.14 * 20.25
Surface Area of one base = 63.585 square inches
Surface Area of both bases = 2 * 63.585
Surface Area of both bases = 127.17 square inches
Total surface area to cover = Lateral surface area + Surface area of both bases
Total surface area to cover = 288.036 + 127.17
Total surface area to cover = 415.206 square inches
Simone will need approximately 415.206 square inches of patterned paper to cover the entire box.