The generatrix of the cone is 26 cm, and its height is 24 cm. Find the volume of the cone.

Consider a right-angled triangle formed by the height of the cone, its generatrix and the radius of the base. Height and radius of the base – legs, forming – hypotenuse. Therefore, by the Pythagorean theorem:

h ^ 2 + r ^ 2 = l ^ 2.

Knowing that the generatrix of this cone is 26 cm, the height is 24 cm, we find the radius of the base:

r ^ 2 = l ^ 2 – h ^ 2 = 26 ^ 2 – 24 ^ 2 = 676 – 576 = 100 = 10^2;

r = 10 cm.

The volume of the cone is equal to one third of the product of the area of its base by the height:

V = nr2 * h / 3 = n * 10 ^ 2 * 24/3 = n * 100 * 24/3 = 800n ≈ 2513.27 cm3.