13 cm
d = 10 cm
Find the length of the height of the cone.
To find the length of the height of the cone, we can use the Pythagorean theorem. The height (h) of the cone, the radius (r) of the base, and the slant height (s) form a right triangle.
We know that the radius (r) is half of the diameter (d), so r = d/2 = 10 cm/2 = 5 cm.
Using the Pythagorean theorem, we have:
s^2 = r^2 + h^2.
Since we are given that the slant height (s) is 13 cm, we can substitute this into the equation:
13^2 = 5^2 + h^2.
169 = 25 + h^2.
Subtracting 25 from both sides:
144 = h^2.
Taking the square root of both sides:
h = sqrt(144).
Therefore, the length of the height of the cone is h = 12 cm.