What is the height of the right circular cone 15 in slant height 14 in height and 12 in diameter

Answer 1

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.