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
whats the correct answer
The correct answer is 206.55 square inches.
To find the surface area of the cylinder, we need to find the lateral surface area and the top and bottom circular areas.
Lateral surface area = height * circumference of the base
Lateral surface area = 10.2 * (2 * 3.14 * 4.5)
Lateral surface area = 10.2 * 28.26
Lateral surface area = 288.852 square inches
Top circular area = (3.14 * 4.5^2)
Top circular area = 63.585 square inches
Bottom circular area = (3.14 * 4.5^2)
Bottom circular area = 63.585 square inches
Total surface area = Lateral surface area + 2 * Top circular area
Total surface area = 288.852 + 2 * 63.585
Total surface area = 288.852 + 127.17
Total surface area = 416.022 square inches
Therefore, Simone will need 416.022 square inches of paper to cover the entire box.