The total surface area of the cylinder is 500π cm². Its base diameter is 20 cm. Calculate the volume of the cylinder.

The total surface area of the cylinder is S = 2πr (h + r), and the volume of the cylinder is: V = πr²h.
Knowing the total surface area, we find h.
h = S / 2πr – r. According to the conditions of the problem, S = 500π, and r = 20: 2 = 10, then h = 500π / 2π * 10 – 10 = 15 (cm).
Now let’s find the volume of the cylinder:
V = π r²h,
V = π * 10² * 15 = π * 100 * 15 = 1500π (cm³).
Answer: V = 1500π (cm³).