Find the radius of the cone if its height is 2 cm, and the generatrix is 9 cm.

In order to obtain a cone, it is necessary to turn a right-angled triangle around one of its legs.

This triangle, in this case, will be half the axial section of this cone. For convenience, we will designate it as ABC, where:

AB – Generating, the length of which is 9 cm;

ВС – height, the length of which is 2 cm;

AC is the radius of the base.

Since the triangle is rectangular, we apply the Pythagorean theorem:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2;

AC ^ 2 = 92 – 22 = 81 – 4 = 77;

AC = √77 = 8.8 cm.

Answer: The radius of the base of the cone is 8.8 cm.