Find the volume of the cone, the generatrix of which = 13cm, and the base diameter = 10cm.

The height of the cone, the radius of its base and the generatrix form a right-angled triangle, in which the height and radius are the legs, and the generatrix is the hypotenuse. By the Pythagorean theorem, we can find the height of the cone:

h ^ 2 = L ^ 2 – r ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144 = 12 ^ 2;

h = 12 cm.

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

V = Ssc * h / 3 = nr ^ 2 * h / 3 = n * 5 ^ 2 * 12/3 = n * 25 * 12/3 = 100n ≈ 314.16 cm3 – the desired volume of the cone.