a cone has a diameter of 12 inches a height of 14 inches and a slant hieght of 15 inches what is the height of the right circular cone

Answer 1

The height of the right circular cone can be calculated using the Pythagorean theorem.

Given:
Diameter of the cone = 12 inches
Radius of the cone (half of the diameter) = 6 inches
Slant height of the cone = 15 inches

Let's draw a right triangle with the height (h) as one side, the slant height (l) as the hypotenuse, and the radius (r) as the other side.

Using the Pythagorean theorem:
h^2 + r^2 = l^2

Substituting the values:
h^2 + 6^2 = 15^2
h^2 + 36 = 225
h^2 = 225 - 36
h^2 = 189

Taking the square root of both sides:
h = √189

Simplifying the square root:
h ≈ 13.75 inches

Therefore, the height of the right circular cone is approximately 13.75 inches.