# The height of the cylinder is 3 times the radius of the base, and the total surface

October 3, 2021 | education

| **The height of the cylinder is 3 times the radius of the base, and the total surface area is 288п cm2. Determine the base radius and height.**

Let the radius of the cylinder be R cm, then the height of the cylinder is 3 * R cm.

The base area of the cylinder will be equal to:

Sb = n * R ^ 2 cm2.

The lateral surface area of the cylinder is:

Side = 2 * n * R * 3 * R = 6 * n * R ^ 2 cm2.

The total surface area of the cylinder is:

S floor = 2 * S main + S side = 2 * n * R ^ 2 + 6 * n * R ^ 2 = n * 288.

8 * n * R ^ 2 = n * 288.

R ^ 2 = 36.

R = 6 cm.

Then h = 3 * 6 = 18 cm.

Answer: The radius of the circle is 6 cm, the height is 18 cm.

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