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
4.5 top
1.2h
4.5 bottom
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
To find the total surface area of the cylindrical storage box, we need to find the surface area of the top and bottom circle, as well as the lateral surface area.
Top and bottom circles:
Area = πr^2
Area = 3.14 x 4.5^2
Area = 3.14 x 20.25
Area = 63.585 square inches (approx. 63.59 square inches)
Lateral surface area:
Area = 2πrh
Area = 2 x 3.14 x 4.5 x 10.2
Area = 2 x 3.14 x 45.9
Area = 288.276 square inches (approx. 288.28 square inches)
Total surface area:
Total SA = 2(top and bottom circles) + lateral surface area
Total SA = 2(63.59) + 288.28
Total SA = 127.18 + 288.28
Total SA = 415.46 square inches
Therefore, Simone will need 415.46 square inches of paper to cover the entire box. So the closest answer choice is 415.42 square inches.