The lateral surface of the cylinder is three times the area of its base. Find the ratio of the height

The lateral surface of the cylinder is three times the area of its base. Find the ratio of the height of the cylinder to the radius of its base.

Let the radius of the circle at the base of the cylinder OA = R cm, and the height of the cylinder OO1 = H cm.

Then the area of the lateral surface of the cylinder will be equal to:

Sside = 2 * n * R * H cm2.

The base area of the cylinder will be equal to:

Sb = n * R ^ 2 cm2.

By the condition S side / S main = 3.

Then: (2 * n * R * H) / (n * R ^ 2) = 3.

(2 * H) / R = 3,

H / R = 3/2 = 1.5.

Answer: The ratio of the height of the cylinder to the radius of its base is 1.5.