Find the length of the height of a Cone.
The diameter is 10.
The slant height of the tringle is 13.
To find the height of a cone, we can use the Pythagorean theorem.
In a right triangle formed by the height, slant height, and the radius (half of the diameter), we can apply the Pythagorean theorem:
(hypotenuse)^2 = (base)^2 + (height)^2
In this case, the slant height is the hypotenuse and the radius is the base.
Therefore,
(13)^2 = (radius)^2 + (height)^2
Since the diameter is given as 10, the radius is half of that, which is 5.
Substituting the values into the equation, we have:
(13)^2 = (5)^2 + (height)^2
169 = 25 + (height)^2
(height)^2 = 169 - 25
(height)^2 = 144
Taking the square root of both sides, we get:
height = √144
height = 12
Therefore, the length of the height of the cone is 12 units.