Question
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.
Answers
GPT 3.5
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.
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.