What is the height of the right circular cone?

1 answer

To determine the height of a right circular cone, you will typically need additional information, such as the radius of the base and the slant height or the volume of the cone.

The height \( h \) of the cone can be calculated using the following formulas, depending on the given information:

  1. Using volume: If you know the volume \( V \) of the cone and the radius \( r \) of the base, you can use the formula for the volume of a cone: \[ V = \frac{1}{3} \pi r^2 h \] Rearranging this formula gives: \[ h = \frac{3V}{\pi r^2} \]

  2. Using slant height: If you know the radius \( r \) of the base and the slant height \( l \), you can use the Pythagorean theorem: \[ l^2 = r^2 + h^2 \] Rearranging this gives: \[ h = \sqrt{l^2 - r^2} \]

To provide the height of the cone, please specify which dimensions or values are known!