What is the height of the right circular cone?

Question

The cone has a slant height of 9 cm, and a radius of 11 cm.

Answer 1

To find the height of the right circular cone, we can use the Pythagorean theorem.

The slant height, radius, and height form a right triangle. Let's label the height as h.

By the Pythagorean theorem, we have:

radius^2 + height^2 = slant height^2
11^2 + h^2 = 9^2
121 + h^2 = 81
h^2 = 81 - 121
h^2 = -40

Since the square of a real number cannot be negative, there is no real solution for h^2. This means that the given measurements of a slant height of 9 cm and a radius of 11 cm do not correspond to a valid right circular cone.