A student says the two cylinders below have the same surface area. Explain the student’s error. (Use 3.14 for π.) 3in wide, 10in tall for one cylinder. one cylinder is 10in wide, and 3in tall.

Answer 1

The student's error lies in assuming that two cylinders with different dimensions can have the same surface area. The surface area of a cylinder is calculated using the formula 2πrh + 2πr^2, where r is the radius and h is the height of the cylinder.

For the first cylinder with dimensions 3in wide and 10in tall:
r = 3in / 2 = 1.5in
h = 10in

Surface area = 2(3.14)(1.5)(10) + 2(3.14)(1.5)^2
Surface area = 94.2 + 14.13
Surface area = 108.33 square inches

For the second cylinder with dimensions 10in wide and 3in tall:
r = 10in / 2 = 5in
h = 3in

Surface area = 2(3.14)(5)(3) + 2(3.14)(5)^2
Surface area = 94.2 + 157
Surface area = 251.2 square inches

Therefore, the two cylinders do not have the same surface area. The cylinder with dimensions 10in wide and 3in tall actually has a surface area of 251.2 square inches, which is larger than the surface area of the cylinder with dimensions 3in wide and 10in tall (108.33 square inches).