The diameter of the base of the cone is 30 and the length of the generatrix is 25. Find the volume of the cone.

univerkov | July 4, 2021 | education

Consider a right-angled triangle SOB, in which the angle O is equal to 900, since SO is the height of the cone, the leg OB is equal to half the diagonal of the circle at the base of the cone, OB = AB / 2 = 30/2 = 15 cm, and the hypotenuse SB is equal to the generatrix of the cone. Then, by the Pythagorean theorem, the leg SO will be equal to:

SO ^ 2 = SB ^ 2 – OB ^ 2 = 625 – 225 = 400.

SO = 20 cm.

The volume of the cone is equal to: V = Sosn * SO / 3.

Determine the area of the base of the cone.

Sop = n * R ^ 2 = n * 15 ^ 2 = 225 * n cm2.

Then V = 225 * n * 20/3 = 1500 * n cm3.

Answer: The volume of the cone is 1500 * n cm3.

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