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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 PI)
the angles are 4.5, 10.2, and 4.5
A. 74.16 square inches
B. 206.55 square inches
C. 415.42 square inches
D. 648.57 square inches
To find the total surface area of the box, we need to find the area of the two circular bases and the lateral surface area.
1. Area of one circular base:
A = πr^2
A = 3.14 * 4.5^2
A = 3.14 * 20.25
A = 63.585 square inches
Since there are two circular bases, the total area for the circular bases is:
2 * 63.585 = 127.17 square inches
2. Lateral surface area:
A = 2πrh
A = 2 * 3.14 * 4.5 * 10.2
A = 286.92 square inches
To find the total surface area, add the area of the two circular bases and the lateral surface area:
127.17 + 286.92 = 414.09 square inches
Therefore, Simone will need 414.09 square inches of paper to cover the entire box. Rounded to the nearest hundredth, this is approximately 415.42 square inches.
So, the answer is C. 415.42 square inches.