A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
one cylinder is 3in diameter and height 10in
the other cylinder is 10 in diameter and height 3 in
(2 points)
The student's error is assuming that cylinders with the same surface area will have the same dimensions. However, the surface area of a cylinder is calculated using the formula 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.
For the first cylinder (3in diameter, 10in height):
- Radius (r) = 3in/2 = 1.5in
- 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 (10in diameter, 3in height):
- Radius (r) = 10in/2 = 5in
- 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 student's error was assuming that cylinders with the same surface area will have the same dimensions.