A student says the two cylinders below have the same surface area. Explain the student's error.(use 3.14 for pi)
cylinder 1 ( height 10 inches, with a radius of 3)
cylinder 2 ( height 3 inches, with a radius of 10)
The student's error is in assuming that the surface area of a cylinder is only dependent on the height and radius of the cylinder. In reality, the surface area of a cylinder is calculated using the formula 2*pi*r*h + 2*pi*r^2.
For cylinder 1:
Surface area = 2*3.14*3*10 + 2*3.14*3^2
Surface area = 188.4 + 56.52
Surface area = 244.92 square inches
For cylinder 2:
Surface area = 2*3.14*10*3 + 2*3.14*10^2
Surface area = 188.4 + 628
Surface area = 816.4 square inches
Therefore, the two cylinders do not have the same surface area. Cylinder 2 actually has a larger surface area than cylinder 1.