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, we need to calculate the lateral surface area (the side of the cylinder) and the two circular bases.
Lateral surface area = 2πrh
Lateral surface area = 2 * 3.14 * 4.5 * 10.2
Lateral surface area = 289.08 square inches
Circular base area = πr^2
Circular base area = 3.14 * 4.5^2
Circular base area = 3.14 * 20.25
Circular base area = 63.63 square inches
Now we add the lateral surface area and the two circular base areas to get the total surface area of the cylinder:
Total surface area = Lateral surface area + 2 * Circular base area
Total surface area = 289.08 + 2(63.63)
Total surface area = 289.08 + 127.26
Total surface area = 416.34 square inches
Therefore, Simone will need 416.34 square inches of patterned paper to cover the entire box.