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 height of the cylinder. In 3-5 sentences, explain what would happen to the surface area if she did both these things.

Answer 1

If Jordyn triples both the radius and height of the cylinder, the surface area of the cylinder would increase significantly. The surface area of a cylinder is calculated using the formula: 2πrh + 2πr^2. Tripling the radius would result in a 9 times increase in the surface area of the circular ends (2πr^2), as it is proportional to the square of the radius. Tripling the height would also result in a 3 times increase in the lateral surface area (2πrh). Therefore, the total surface area of the cylinder would increase by a factor of 27 (3 x 9) if both the radius and height are tripled.