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?
To calculate the total surface area of the cylinder, we need to find the lateral surface area and the surface area of the two circular bases.
1. Lateral Surface Area:
To find the lateral surface area of a cylinder, we use the formula:
Lateral Surface Area = 2 * π * r * h
Where r is the radius and h is the height of the cylinder.
Plugging in the values:
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 288.12 square inches
2. Surface Area of the Bases:
To find the surface area of one circular base, we use the formula:
Surface Area of a Circle = π * r^2
Since there are two circular bases, the total surface area of the bases is:
Total Surface Area of Bases = 2 * π * 4.5^2
Total Surface Area of Bases = 127.23 square inches
3. Total Surface Area of the Cylinder:
Total Surface Area = Lateral Surface Area + Total Surface Area of Bases
Total Surface Area = 288.12 + 127.23
Total Surface Area = 415.35 square inches
Therefore, Simone would need 415.35 square inches of patterned paper to cover the entire cylinder.