A student says the two cylinders below have the same surface area. Explain the student's error.

Question

A student says the two cylinders below have the same surface area. Explain the student's error.

A cylinder has a base diameter measuring 6 inches and a height measuring 8 inches. A second cylinder has a base diameter measuring 8 inches and a height measuring 6 inches.

Answer 1

The student's error is that the two cylinders do not have the same surface area. The surface area of the first cylinder is 6π x 8 = 48π, while the surface area of the second cylinder is 8π x 6 = 48π.