Find the length of the height of the cone with a diameter of 10 cm and slant height of 13 cm height
To find the height of a cone, we can use the Pythagorean theorem as applied to the right triangle formed by the height of the cone, the slant height, and the radius of the base.
Given the diameter of the cone is 10 cm, the radius (r) of the base of the cone is half of that, which is 5 cm. The slant height (l) is given as 13 cm. We can denote the height of the cone as h.
We can describe the relationship between the slant height, the height, and the radius of the base using the Pythagorean theorem:
l² = r² + h²
Now plug in the values for l and r:
13² = 5² + h²
169 = 25 + h²
Now solve for h²:
h² = 169 - 25
h² = 144
Taking the square root of both sides to find the value of h:
h = √144
h = 12
So the height of the cone is 12 cm.