The radius of the base of the cylinder is 5 cm, the lateral surface area is twice the area of the base. find the volume of the cylinder.
1. The formula for the volume of a cylinder V = Sb * h, where h is the height of the cylinder, and Sb is the area of the base of the cylinder.
Sbn = nR ^ 2, where R is the radius of the base.
By the condition of the problem, the area of the lateral surface is Sbok = Sosn * 2.
Sbok = Rosn * h, where Rosn is the perimeter of the base. Rosn = 2pR.
2nR * h = nR ^ 2 * 2.
Let’s find the height h and the base area Sbase:
h = nR ^ 2 * 2 / 2nR = R = 5 (cm);
Sb = n * 52 = 25p (cm2).
Find the volume of the cylinder:
V = 25p * 5 = 125p ≈ 392.5 (cm3).
Answer: the volume of the cylinder is 392.5 cm3.
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