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.
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.
