A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
the cylinder 1 has a diameter of 3 in and height of 10 in
the cylinder 2 has a diameter 10 in and height of 3 in
The student's error is that surface area of a cylinder is not solely dependent on the diameter and height, but also on the formula used to calculate it.
The surface area of a cylinder is given by the formula:
2πr^2 + 2πrh
For cylinder 1:
- Radius (r) = diameter/2 = 3/2 = 1.5 in
- Surface Area = 2(3.14)(1.5)^2 + 2(3.14)(1.5)(10)
= 2(3.14)(2.25) + 2(3.14)(15)
= 28.26 + 94.2
= 122.46 square inches
For cylinder 2:
- Radius (r) = diameter/2 = 10/2 = 5 in
- Surface Area = 2(3.14)(5)^2 + 2(3.14)(5)(3)
= 2(3.14)(25) + 2(3.14)(15)
= 157 + 94.2
= 251.2 square inches
Therefore, the two cylinders do not have the same surface area. Cylinder 2 has a larger surface area compared to cylinder 1.