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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