Find the volume of the cone if the generatrix is 13 cm and the diameter is 24.

The radius of the circle at the base r = d / 2 = 24/2 = 12 cm, the generatrix l = 13 cm and the height of the cone h form a right-angled triangle.

Find the height h:

h = √ (l ^ 2 – r ^ 2) = √ (13 ^ 2 – 12 ^ 2) = √25 = 5 cm.

Cone volume:

V = (Sosn * h) / 3 = (n * r ^ 2 * h) / 3 = (3.14 * 6 ^ 2 * 5) / 3 = 188.4 cm ^ 3.

Answer: 188.4 cm ^ 3.