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.)
(1 point)
Responses
74.16 square inches
74.16 square inches
206.55 square inches
206.55 square inches
415.42 square inches
415.42 square inches
648.57 square inches
648.57 square inches
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To calculate the total surface area of the cylinder, we need to find the lateral surface area and the area of the two circular ends.
Lateral surface area = 2πrh
= 2(3.14)(4.5)(10.2)
= 288.36 square inches
Area of two circular ends = 2πr^2
= 2(3.14)(4.5)^2
= 127.35 square inches
Total surface area = Lateral surface area + Area of two circular ends
= 288.36 + 127.35
= 415.71 square inches
Therefore, Simone will need 415.71 square inches of paper to cover the entire box.
The closest option in the list is 415.42 square inches.