A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.) 3in wide 10in tall, 10in wide 3in tall.

Answer 1

The student's error is that they are assuming the surface area of a cylinder is only dependent on the height and width of the cylinder.

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

In the case of the two cylinders provided:
- For the first cylinder: r = 3/2 = 1.5 inches, h = 10 inches.
Surface area = 2 * 3.14 * (1.5)^2 + 2 * 3.14 * 1.5 * 10 ≈ 94.2 square inches.

- For the second cylinder: r = 10/2 = 5 inches, h = 3 inches.
Surface area = 2 * 3.14 * (5)^2 + 2 * 3.14 * 5 * 3 ≈ 157 square inches.

Therefore, the surface areas of the two cylinders are not the same. The second cylinder has a larger surface area compared to the first cylinder.