Ask a New Question
Menu

Which is longer in a cone, the height or slant height? Which do you use in the Volume for a Cone Formula?

Which is longer in a sphere, the radius or the diameter? Which do you use in the Volume for a Sphere Formula?

1 answer

In a cone:

  1. Height vs. Slant Height: The slant height of a cone is always longer than the height, unless the height is zero (in which case it would not be a cone).

  2. Volume Formula: In the volume formula for a cone, you use the height. The formula for the volume \( V \) of a cone is given by:

    \[ V = \frac{1}{3} \pi r^2 h \]

    where \( r \) is the radius of the base and \( h \) is the height of the cone.

In a sphere:

  1. Radius vs. Diameter: The diameter of a sphere is always longer than the radius, as the diameter is twice the radius. Specifically, the diameter \( d \) is related to the radius \( r \) by the equation \( d = 2r \).

  2. Volume Formula: In the volume formula for a sphere, you use the radius. The formula for the volume \( V \) of a sphere is given by:

    \[ V = \frac{4}{3} \pi r^3 \]

    where \( r \) is the radius of the sphere.

In summary, for a cone, the slant height is longer, and you use the height to calculate volume. For a sphere, the diameter is longer, and you use the radius to calculate volume.