The height of the cone is 3m and the generatrix is 5m. Find the volume of the cone.

A cone is a geometric body formed by the rotation of a pteangle around its leg.
The volume of any kind of cone is calculated by the formula:
V = 1/3 * S * H, where:
V is the volume of the cone;
S – base area;
H – height.
In order to calculate the area of the base, we find its radius. To do this, apply the generatrix formula:
L ^ 2 = R ^ 2 + H ^ 2;
R ^ 2 = L ^ 2 – H ^ 2;
R ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;
R = √16 = 4 m.
Since the base of the cone is a circle, the area of its base is calculated using the formula for the area of a circle:
S = πR ^ 2;
S = 3.14 * 16 = 50.24 m2.
V = 1/3 * 50.24 * 3 = 50.24 m3.
Answer: the volume of the cone is 50.24 m3.