Question
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(7th Grade Math Formula Chart: Ctrl + select to open in a new tab)
A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
(2 points)
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The student's error lies in the fact that they only calculated the lateral surface area of the cylinders and ignored the total surface area. The lateral surface area is the area of the curved part of the cylinder, while the total surface area includes the top and bottom bases as well.
To calculate the lateral surface area of a cylinder, the formula is 2πrh, where r is the radius and h is the height.
To calculate the total surface area of a cylinder, the formula is 2πr(r + h), where r is the radius and h is the height.
If we compare two cylinders with the same lateral surface area but different heights, the one with the greater height will have a greater total surface area. Therefore, the student's assumption that the two cylinders have the same surface area is incorrect.