The area of the base of the cone is 64 / п, the area of the axial section of the cone is 30. Find the volume of the cone.

Let’s use the picture to solve the problem.

By condition, the area of the base of the cone is 64 / p. Knowing the area of the base, we find the radius of the circle of the base.

Sosn = n * R ^ 2 = 64 / n.

R2 = 64 / n ^ 2.

R = 8 / p.

Then the diameter of the circle BC = 16 / n.

The axial section of the cone is a triangle ABC whose area is 30 cm2.

SABC = (AO * BC) / 2.

30 = (AO * 16 / n) / 2.

AO = 60 * n / 16 = 15 * n / 4.

Then the volume of the cone will be equal to:

V = (1/3) * AO * Sop = (1/3) * (15 * n / 4) * (64 / n) = (15 * 64) / (3 * 4) = 80 cm3.

Answer: The volume of the cone is 80 cm3.