The lateral surface area of the cylinder is 50P, and the base diameter is 10. Find the height of the cylinder.

Let a cylinder be given, at the base of which lies a circle with a diameter D = 10. The area of the lateral surface of the cylinder S is determined as the product of the circumference of the base π ∙ D by its height H, that is, S = π ∙ D ∙ H, where π ≈ 3.14. It is known from the problem statement that the area of the lateral surface of the cylinder is S = 50 ∙ π. Equating the right-hand sides of these equalities, we obtain the equation π ∙ D ∙ H = 50 ∙ π, from which we find the height of the cylinder H = (50 ∙ π): (π ∙ D); H = 50: D; H = 50: 10; H = 5.
Answer: The height of this cylinder is 5.