The height of the cylinder is 10 cm greater than the radius of the base, and the axial

The height of the cylinder is 10 cm greater than the radius of the base, and the axial cross-sectional area is 22 cm2. Find the dimensions of the cylinder.

Let the radius of the base be x cm, then the height of the cylinder is (x + 10) cm.Let’s use the formula for the area of a rectangle and compose the equation:
2x * (x + 10) = 22
2x² + 20x – 22 = 0
x² + 10x – 11 = 0
By Vieta’s theorem, the roots of the quadratic equation are obtained:
x1 = -11, x2 = 1.
The negative root of the equation does not correspond to the condition of the problem.
r = 1 (cm);
h = 11 (cm).
Answer: the radius of the base is 1 cm, the height of the cylinder is 11 cm.