A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
A cylinder has a base diameter measuring 3 inches and a height measuring 10 inches. A second cylinder has a base diameter measuring 10 inches and a height measuring 3 inches.
The student is incorrect in assuming that the two cylinders have the same surface area. Surface area of a cylinder is calculated using the formula:
Surface Area = 2πr^2 + 2πrh
For the first cylinder with a base diameter of 3 inches and a height of 10 inches:
- radius (r) = diameter/2 = 3/2 = 1.5 inches
- Surface Area = 2(3.14)(1.5)^2 + 2(3.14)(1.5)(10) = 47.1 + 94.2 = 141.3 square inches
For the second cylinder with a base diameter of 10 inches and a height of 3 inches:
- radius (r) = diameter/2 = 10/2 = 5 inches
- Surface Area = 2(3.14)(5)^2 + 2(3.14)(5)(3) = 157 + 94.2 = 251.2 square inches
Therefore, the two cylinders do not have the same surface area. The second cylinder actually has a greater surface area than the first cylinder.