Question
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
Answers
GPT 3.5
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.
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.