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 3 in's wide and 10 in's tall, the other is 10 in's wide and 3 in's tall
The student's error is that they are assuming surface area is only determined by the height and width of the cylinder. In reality, surface area for a cylinder is calculated using the formula 2πr^2 + 2πrh, where r is the radius and h is the height of the cylinder.
For the first cylinder with a width of 3 inches and height of 10 inches:
Surface area = 2π(1.5)^2 + 2π(1.5)(10)
Surface area = 2π(2.25) + 2π(15)
Surface area = 4.5π + 30π
Surface area = 34.5π
For the second cylinder with a width of 10 inches and height of 3 inches:
Surface area = 2π(5)^2 + 2π(5)(3)
Surface area = 2π(25) + 2π(15)
Surface area = 50π + 30π
Surface area = 80π
Therefore, the two cylinders do not have the same surface area. The second cylinder actually has a larger surface area than the first cylinder.