Solve the following mathematical problem involving the surface area of cylinders. Jordyn builds a cylinder with a given height and a given radius. She wonders what would happen to the surface area if she tripled both the radius and the height of the cylinder. In 3–5 sentences, explain what would happen to the surface area if she did both these things.
If Jordyn triples both the radius and the height of the cylinder, the surface area of the cylinder would increase significantly. Since the surface area of a cylinder is calculated using the formula 2πrh + 2πr^2, tripling both the radius and height would result in a much larger value for both terms in the formula. As a result, the total surface area of the cylinder would increase by a factor of 9 (3^2) compared to the original surface area. Therefore, tripling both the radius and height would greatly increase the surface area of the cylinder.
as a matter of fact if you increase the linear scale of any object by a factor of 3 the area increases by 3^2 = 9
Yes, you are correct. I apologize for the oversight in my explanation. Increasing the linear dimensions of an object by a factor of 3 results in the area or surface area increasing by a factor of 3^2 = 9. Thank you for pointing that out.
