The height of the cylinder is 10 cm greater than the radius of the base.

The height of the cylinder is 10 cm greater than the radius of the base. The total surface area is 264 cm (2). Find the radius of the base of the cylinder?

The total surface area of ​​the cylinder is equal to the sum of the areas of the two bases and the lateral surface: S total = S side + 2S main.
Sosn = πr ^ 2, where r is the radius of the cylinder base;
Side = h * l, where h is the height of the cylinder, l is the circumference of the base, equal to 2πr.
By condition, the height of the cylinder is 10 cm greater than the radius of the base, which means h = r + 10, and the total surface area is 264 cm2. Let’s make the equation:
Sful = Sside + 2Sn = h * l + 2πr ^ 2 = (r + 10) * 2πr + 2πr ^ 2 = 2πr ^ 2 + 20πr + 2πr ^ 2 = 4πr ^ 2 + 20πr;
4πr ^ 2 + 20πr = 264;
4πr ^ 2 + 20πr-264 = 0.
Dividing both sides of the equation by 4π, we get:
r ^ 2 + 5r-21.0085 = 0.
Find the discriminant: D = b ^ 2-4ac = 25 + 4 * 21.0085 = 109.034.
√D = √109.034 = 10.442.
r1 = (- b-√D) / 2a = -5-10.442 / 2 = -7.721 – does not satisfy the condition of a positive value of the radius.
r2 = (- b + √D) / 2a = -5 + 10.442 / 2 = 2.721.
Therefore, the radius of the base of this cylinder is 2.721 cm.