To find the total surface area of the cylinder, we need to calculate the lateral surface area and the area of the two circular bases separately.
The lateral surface area of a cylinder is given by the formula: 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2
Lateral Surface Area = 289.08 square inches
The area of one circular base (which we need to cover as well) is given by the formula: πr^2, where r is the radius.
Area of One Base = 3.14 * 4.5^2
Area of One Base = 63.585 square inches
Since there are two circular bases, the total area of both bases is: 2 * 63.585 = 127.17 square inches
Now, add the lateral surface area and the total area of the bases to get the total surface area:
Total Surface Area = Lateral Surface Area + Total Area of Both Bases
Total Surface Area = 289.08 + 127.17
Total Surface Area = 416.25 square inches
Therefore, Simone will need 416.25 square inches of patterned paper to cover the entire box. All that is closest to this from the options provided is 415.42 square inches.
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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 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
1 answer
1 answer