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 entire box, we need to calculate the lateral surface area of the cylinder and the area of the two circular bases.
1. Lateral Surface Area of the Cylinder:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 289.08 square inches
2. Area of the Two Circular Bases:
Area of each circular base = πr^2
Area of each circular base = 3.14 * (4.5)^2
Area of each circular base = 3.14 * 20.25
Area of each circular base = 63.585 square inches
Total area of both circular bases = 2 * 63.585 = 127.17 square inches
Therefore, the total surface area of the entire box is:
Total Surface Area = Lateral Surface Area + Total area of both circular bases
Total Surface Area = 289.08 + 127.17
Total Surface Area = 416.25 square inches
Simone will need 416.25 square inches of patterned paper to cover the entire box.