Question
A student says the two cylinders below have the same surface. Explain the students error. (Use 3.14 for pi)
Answers
GPT 3.5
The student's error lies in assuming that the surface area of a cylinder depends only on the height and radius of the cylinder, and not on the shape of the cylinder itself. In reality, the surface area of a cylinder is calculated using the formula:
Surface Area = 2 * pi * radius * (radius + height)
While the two cylinders in question may have the same height and radius, their shapes are different. Cylinder A has a straight and flat top, while Cylinder B has a curved dome-shaped top. As a result, Cylinder B will have a larger surface area than Cylinder A, even though they have the same height and radius.
Therefore, the student's assumption that the two cylinders have the same surface area is incorrect.
Surface Area = 2 * pi * radius * (radius + height)
While the two cylinders in question may have the same height and radius, their shapes are different. Cylinder A has a straight and flat top, while Cylinder B has a curved dome-shaped top. As a result, Cylinder B will have a larger surface area than Cylinder A, even though they have the same height and radius.
Therefore, the student's assumption that the two cylinders have the same surface area is incorrect.