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A student says the two cylinders below have the same surface area. Explain the student's error.
(Use 3.14 for PI.)
The student's error is assuming that two cylinders have the same surface area simply based on their heights and base radii being equal. Surface area of a cylinder is given by the formula 2πr(r+h), where r is the radius of the base and h is the height of the cylinder.
Let's say Cylinder 1 has a radius of 5 units and a height of 10 units, and Cylinder 2 has a radius of 10 units and a height of 5 units.
Surface area of Cylinder 1 = 2π(5)(5+10) = 2π(5)(15) = 150π
Surface area of Cylinder 2 = 2π(10)(10+5) = 2π(10)(15) = 300π
Even though the heights and base radii are the same for both cylinders, their surface areas are different. Therefore, the student's assumption that the two cylinders have the same surface area is incorrect.