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 10.5 inches. The cylinders net is shown below. How much paper will Simone need to cover the entire box? Use 3.14 for pi
To find the surface area of the cylinder, we need to calculate the area of the two circular ends and the lateral surface area.
1. Area of one circular end:
A = πr^2
A = 3.14 * (4.5)^2
A = 3.14 * 20.25
A = 63.585 square inches
2. Area of both circular ends:
Total area = 2 * 63.585
Total area = 127.17 square inches
3. Lateral surface area:
Lateral area = 2 * π * r * h
Lateral area = 2 * 3.14 * 4.5 * 10.5
Lateral area = 296.82 square inches
4. Total surface area of the cylinder:
Total surface area = 127.17 + 296.82
Total surface area = 423.99 square inches
Therefore, Simone will need approximately 424 square inches of patterned paper to cover the entire box.