A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.)
top 3 top 10
height 10 height 3
The student's error lies in assuming that two figures have the same surface area simply because they have the same numerical value in different dimensions (in this case, the top circumference). However, surface area is not only dependent on one dimension but also on the other dimensions of the object.
In this case:
- The surface area of the top cylinder would be 2πr1h1 = 2(3.14)(1.5)(10) = 94.2 square units.
- The surface area of the bottom cylinder would be 2πr2h2 = 2(3.14)(5)(3) = 94.2 square units.
Despite having different dimensions for the top and height of the two cylinders, they cannot be considered to have the same surface area as their surface areas are different.