A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
1. radius=3
Height = 10
2. radius= 10
Height 3
The student's error lies in assuming that the surface area of a cylinder is solely determined by the radius of the base and not affected by the height of the cylinder.
To calculate the surface area of a cylinder, you need to consider both the curved surface area and the area of the two bases.
For Cylinder 1:
Curved surface area = 2πrh = 2 * 3.14 * 3 * 10 = 188.4
Base area = πr^2 = 3.14 * 3^2 = 28.26
Total surface area = Curved surface area + 2(Base area) = 188.4 + 2(28.26) = 244.92
For Cylinder 2:
Curved surface area = 2πrh = 2 * 3.14 * 10 * 3 = 188.4
Base area = πr^2 = 3.14 * 10^2 = 314
Total surface area = Curved surface area + 2(Base area) = 188.4 + 2(314) = 816.4
Therefore, the two cylinders do not have the same surface area. The surface area of Cylinder 2 is significantly larger than that of Cylinder 1 due to the larger base area and smaller height.