The height of the cylinder is 6 cm, and the area of its lateral surface is half the area of its full surface.
| May 28, 2021 | education
The height of the cylinder is 6 cm, and the area of its lateral surface is half the area of its full surface. find the volume of the cylinder.
Let us use the formulas for the lateral surface area and the total surface of the cylinder.
Side = 2 * n * R * OO1 = 12 * n * R cm2.
Spov = Sbok + 2 * Son = 12 * n * R + 2 * n * R ^ 2 cm2.
By condition, Sпов = 2 * Sides.
12 * n * R + 2 * n * R ^ 2 = 2 * 12 * n * R.
6 * R + R ^ 2 = 12 * R.
R ^ 2 – 6 * R = 0.
R * (R – 6) = 0.
(R – 6) = 0.
R = 6 cm.
Determine the area of the base of the cylinder.
Sbn = n * R ^ 2 = 36 * n cm2.
Then V = Sosn * OO1 = 36 * n * 6 = 216 * n cm3.
Answer: The volume of the cylinder is 216 * n cm3.
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