The sectional area of the cone is 8 cm2, the height of the cone is 2 times greater than the radius of the base

The sectional area of the cone is 8 cm2, the height of the cone is 2 times greater than the radius of the base. Calculate the volume of the cone.

Let the radius of the circle at the base of the cone be AO = R = X cm, then, by condition, the height of the cone is BO = h = 2 * X cm.

Cone diameter AC = 2 * AO = 2 * X cm

The axial section of the cone is an isosceles triangle, the area of which is:

Ssech = AC * ВO / 2 = 2 * X * 2 * X / 2 = 2 * X ^ 2 = 8 cm2.

X2 = 8/2 = 4.

X = 2 cm.

Then AO = R = 2 cm, BO = h = 4 cm.

Let’s define the volume of the cone.

V = π * R2 * h / 3 = π * 4 * 4/3 = 16 * π / 3 cm3.

Answer: The volume of the cone is 16 * π / 3 cm3.