What is the height of the right circular cone 15 in slant height 14 in height and 12 in diameter
To find the height of the right circular cone, we can use the Pythagorean theorem.
Let h be the height of the cone, l be the slant height, and r be the radius (half the diameter).
From the given information, we have:
l = 15 in
h = 12 in
r = 12/2 = 6 in
Using the Pythagorean theorem, we have:
l^2 = r^2 + h^2
Substituting the given values, we get:
15^2 = 6^2 + h^2
225 = 36 + h^2
h^2 = 225 - 36
h^2 = 189
Taking the square root of both sides, we have:
h = √(189)
h ≈ 13.75 in
Therefore, the height of the right circular cone is approximately 13.75 inches.