Final answer:
The surface area of a cylinder can be expressed in terms of the radius by the formula A = 2πr² + 2πrh. Substituting the circumference C for 2πr, and solving for r, we arrive at the equation r = (A - Ch) / C.
Step-by-step explanation:
To solve the formula for the surface area of a cylinder for the radius, we start with the general formula for the surface area of a cylinder, which is A = 2πr² + 2πrh, where A is the surface area, r is the radius, and h is the height. Given that the circumference C is equal to 2πr, we can substitute C for 2πr in the formula which gives us A = Cr + Ch.
To solve for the radius r, we can isolate it on one side of the equation by subtracting Ch from both sides and then dividing both sides by C, leading to the solution r = (A - Ch) / C.