how to find the height of a cone
To find the height of a cone, you will need to know the radius (or diameter) of the base of the cone and the slant height (the distance from the apex of the cone to the edge of the base).
1. First, find the radius of the base of the cone. If you are given the diameter, divide it by 2 to get the radius.
2. Next, use the Pythagorean theorem to find the height. The height (h), radius (r), and slant height (l) of the cone form a right triangle, so you can use the formula:
h^2 + r^2 = l^2
3. Plug in the values you know. For example, if the radius is 5 cm and the slant height is 8 cm:
h^2 + 5^2 = 8^2
h^2 + 25 = 64
h^2 = 64 - 25
h^2 = 39
h = sqrt(39)
4. Calculate the square root of the difference to find the height of the cone.
In this example, the height of the cone would be approximately 6.24 cm.