Question

Janelle and Dante find the surface area of a cylinder. Janelle Find the area of the curved surface A = bh= (8) (18) = 144 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 144 + 2(254.4) 652.8 ft² Dante 8 ft 9 ft Find the area of the curved surface A = Ph= (18T) (8) = 452.4 ft² Then find the area of each base A = πr² = π(9)² = 254.4 ft² Total surface area = 452.4 + 2(254.4) 961.2 ft² A. Is either student correct? Explain. B. Use Appropriate Tools Which method would you use to find the surface area of the cylinder? Is it more efficient than the method used by Janelle and Dante?​

Answer 1

A. Both students are correct. They used different methods, but both methods lead to the correct answer for the total surface area of the cylinder.

B. The most appropriate tool to use to find the surface area of a cylinder is a formula that combines the area of the curved surface and the area of the two bases. The formula is:

Total surface area = 2πr² + 2πrh

where r is the radius of the cylinder and h is the height.

Janelle found the area of the curved surface and the area of each base separately, and then added them together. This is a valid method, but it requires more steps than the formula.

Dante used the formula, but he made a mistake by using the diameter instead of the radius to find the height. The correct height is 9 feet, not 8 feet. However, his final answer is still correct because he used the correct area for the curved surface.

Using the formula is more efficient than Janelle's method because it requires fewer steps and calculations.