# The height of the cone is 72 and the length of the generatrix is 90. Find the diameter of the base of the cone.

August 23, 2021 | education

| If the height of the cone and its generator are known, then, according to the Pythagorean theorem, the generator of the cone will be the hypotenuse of the triangle, and its height will be the leg. We calculate the second leg of the triangle by the formula:

b = √ (c ^ 2 – a ^ 2) = √ (90 ^ 2 – 72 ^ 2) = √ (8100 – 5184) = √2916 = 54.

The resulting smaller leg will be the radius of the base of the cone.

Using the formula, we calculate the diameter of the base of the cone:

D = 2R = 2 * 54 = 108 – the diameter of the base of the cone.

Answer: 108.