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
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1 answer
anonymous
asked anonymously
calendar icon22 hours.
The correct answer is 206.55 square inches.
U sure
I apologize for the confusion. Let me double-check the calculation for you.
The net of the cylinder consists of two circles (top and bottom) and one rectangle (the side). To calculate the total amount of paper needed to cover the entire box, we need to find the area of each of these shapes and add them together.
1. Area of the top and bottom circles:
Area = π * radius^2
= 3.14 * (4.5)^2
= 3.14 * 20.25
≈ 63.585 square inches (for one circle)
Since there are two circles (top and bottom), the total area for the circles is approximately 2 * 63.585 ≈ 127.17 square inches.
2. Area of the rectangle (side):
The height of the cylinder (side) is 10.2 inches, and the length of the side is the circumference of the circle which can be calculated as:
Circumference = 2 * π * radius
= 2 * 3.14 * 4.5
≈ 28.26 inches
Now, the area of the rectangle (side) is:
Area = height * length
= 10.2 * 28.26
≈ 288.252 square inches
Therefore, the total amount of paper Simone will need to cover the entire box is approximately 127.17 (circles) + 288.252 (rectangle) = 415.422 square inches.
Thus, the correct answer is 415.42 square inches. Thank you for your patience.