Question

Find the length of the height of a Cone.
The diameter is 10.
The slant height of the tringle is 13.

Answer 1

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.