Final answer:
To find the height of a cone, given the slant height and radius, use the Pythagorean theorem: h = sqrt(l^2 - r^2). Square the slant height and radius, subtract the latter from the former, and take the square root.
Step-by-step explanation:
To find the height of a cone when you are given the slant height and radius, you can use the Pythagorean theorem. In the case of a right circular cone, the slant height (l), the radius (r), and the vertical height (h) form a right-angled triangle. The radius is the base, the height is the perpendicular side, and the slant height is the hypotenuse of this right-angled triangle.
The formula derived from the Pythagorean theorem is:
h = sqrt(l^2 - r^2)
So, you'll need to square the slant height and the radius, subtract the square of the radius from the square of the slant height, and then take the square root of that result to find the height.
Example: If the slant height of the cone is 10 units and the radius is 6 units, you would calculate the height as follows:
h = sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8 units