Question

A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)

example a : width 3 in, height 10 in
example b: width 10 in, height 3 in

Answer 1

The student's error lies in only considering the dimensions of the cylinders without taking into account the formulas for surface area.

The surface area of a cylinder is calculated using the formula 2πr2 + 2πrh, where r is the radius of the base and h is the height of the cylinder.

For example a:
Radius (r) = width / 2 = 3 / 2 = 1.5 inches
Surface area = 2 * 3.14 * (1.5)2 + 2 * 3.14 * 1.5 * 10
Surface area = 2 * 3.14 * 2.25 + 2 * 3.14 * 15
Surface area = 14.13 + 94.2
Surface area = 108.33 square inches

For example b:
Radius (r) = width / 2 = 10 / 2 = 5 inches
Surface area = 2 * 3.14 * (5)2 + 2 * 3.14 * (5) * 3
Surface area = 2 * 3.14 * 25 + 2 * 3.14 * 15
Surface area = 157 + 94.2
Surface area = 251.2 square inches

Therefore, the two cylinders do not have the same surface area. Example b has a larger surface area than example a.