The radius of the base of the cone is 5 cm, and the generatrix of the cone is 13 cm, find the volume of the cone.

The formula for the volume of the cone is V = 1/3 * Sbn * H = 1/3 * nR ^ 2 * H
Formula for the generator of the cone L = √ (H ^ 2 + R ^ 2)
From the formula for the generator of the cone, we find the height of the cone:
13 = √ (H ^ 2 + 5 ^ 2)
13 = √ (H ^ 2 + 25) – square both sides of the expression to get rid of the root
169 = H ^ 2 + 25
H ^ 2 = 144, so H = 12
All the necessary data for calculating the volume of the cone is now available:
V = 1/3 * nR ^ 2 * H = 1/3 * 3.14 * 5 ^ 2 * 12 = 3.14 * 10 * 4 = 125.6 cm3