Geometry

Using Slant Height Instead of Vertical Height

Students plug the slant height of a cone or pyramid into a volume formula instead of using the perpendicular vertical height.

Quick check

Why students make it

The slant height is often drawn on the outside and labeled clearly, so it feels like the height. Students also mix up volume formulas with lateral surface area formulas.

The rule done right

Use vertical height hh for volume, such as V=13BhV = \frac{1}{3}Bh or V=13πr2hV = \frac{1}{3}\pi r^2h. Use slant height ℓ\ell for lateral surface area, not for volume.

Related resources

volumeconespyramids