The volume of the cylinder is 27. Find the diameter of the base of the cylinder if its total surface area
| February 7, 2021 | education
The volume of the cylinder is 27. Find the diameter of the base of the cylinder if its total surface area is 2 times the lateral surface area.
The volume of the cylinder is: V = Sсн * h = π * R ^ 2 * h.
The area of the lateral surface of the cylinder is: Sside = 2 * π * R * h cm2.
The total surface area of the cylinder is equal to: Sпов = Sbok + 2 * Sсн = 2 * π * R * h + 2 * π * R ^ 2 = 2 * π * R * (h + π * R).
By condition: Spov / Sbok = 2.
2 * π * R * (h + R) / 2 * π * R * h = 2.
(h + R) / h = 2.
h = R.
V = 27 * π = π * R ^ 2 * h = π * R ^ 3.
R ^ 3 = 27.
R = 3 cm.
D = 2 * R = 6 cm.
Answer: c) The base diameter is 6 cm.
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