The radius of the base of the cylinder is 5 cm, the lateral surface area is twice the area of the base.

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.

I.e:

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.