A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
For the first cylinder raiduis is 3 in and height 10 in
For the second one radius is 10 in height is 3 in
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 with radius 3 in and height 10 in:
Surface area = 2π(3)² + 2π(3)(10)
= 2π(9) + 2π(30)
= 18π + 60π
= 78π
For the second cylinder with radius 10 in and height 3 in:
Surface area = 2π(10)² + 2π(10)(3)
= 2π(100) + 2π(30)
= 200π + 60π
= 260π
Therefore, the two cylinders do not have the same surface area. The first cylinder has a surface area of 78π square inches, while the second cylinder has a surface area of 260π square inches. The student has made an error in assuming that the two cylinders have the same surface area.