Question
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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
648.57 square inches
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To find the surface area of the cylindrical storage box, we need to calculate the lateral surface area and the area of the two circular bases.
The lateral surface area can be calculated using the formula: Lateral Surface Area = 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2 * 3.14 * 4.5 * 10.2 = 289.08 square inches
The area of one circular base can be calculated using the formula: Area of a Circle = πr^2
Area of one circular base = 3.14 * (4.5^2) = 3.14 * 20.25 = 63.585 square inches
Since there are two circular bases, we need to calculate the total area of both bases: Total Base Area = 2 * 63.585 = 127.17 square inches
Now, to find the total surface area of the box, we add the lateral surface area and the total base area: Total Surface Area = Lateral Surface Area + Total Base Area
Total Surface Area = 289.08 + 127.17 = 416.25 square inches
Therefore, Simone will need 416.25 square inches of paper to cover the entire box. The closest option provided is 415.42 square inches.
Question
Which 2-dimensional shape is a cross section of both the cylinder and the pyramid?
(1 point)
Responses
circle
circle
rectangle
rectangle
square
square
triangle
triangle
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The cross-section of both a cylinder and a pyramid is a circle.
In the case of a cylinder, any plane parallel to its base will produce a circle as a cross-section.
In the case of a pyramid, any plane parallel to its base and passing through the apex will produce a circle as a cross-section.
Therefore, the correct answer is circle.