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 for one cylinder. one cylinder is 10in wide, and 3in tall.
The student's error lies in their assumption that the surface area of a cylinder is determined only by its height and width. In reality, 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.
For the first cylinder with a width of 3 inches and a height of 10 inches, the radius would be half of the width, so 1.5 inches. Plugging these values into the formula, we get:
2(3.14)(1.5)² + 2(3.14)(1.5)(10) = 28.26 + 94.2 = 122.46 square inches
For the second cylinder with a width of 10 inches and a height of 3 inches, the radius would be half of the width, so 5 inches. Plugging these values into the formula, we get:
2(3.14)(5)² + 2(3.14)(5)(3) = 157 + 94.2 = 251.2 square inches
Therefore, the two cylinders have different surface areas, with the second cylinder having a larger surface area than the first cylinder. Thus, the student's claim that the two cylinders have the same surface area is incorrect.