Height or Slant Height?
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 4 of 62.
A cone and a pyramid each have two lengths that start at the apex, and they are easy to mix up. On the right cones and pyramids of this course, the height drops straight down through the inside of the solid to the centre of the base. The slant height runs down the outside surface.
On this cone the height is 4, dashed, and the slant height is 5, down the side to the rim. The slant is always the longer one: the height, the radius and the slant make a right triangle, and the slant is its hypotenuse.
On a pyramid the slant height runs down the middle of a side face, from the apex to the middle of a base edge. It is the height of that triangle face, which is why surface areas need it. Volumes need the true height.
Challenge
Tap the slant height of the pyramid, then press Check.
Try it yourself
Find the right part on the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Surface Area & Volume
1Solids and Their Parts
Faces, Edges and VerticesPrisms and CylindersPyramids and ConesHeight or Slant Height?Spheres and HemispheresRecap: Parts of Solids4Pyramids
Volume of a PyramidThe Slant HeightHeight From the SlantHeight From the VolumeRecap: Pyramids2Volume of Prisms
Volume of a CuboidVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume3Cylinders
Volume of a CylinderHeight From the VolumeRadius From the VolumeEnough to Find It?Recap: Cylinders6Spheres and Hemispheres
Volume of a SphereHalf a SphereRadius From the VolumeSphere in a CylinderRecap: Spheres9Pyramids and Cones Outside
Surface of a PyramidSlant Height FirstSurface of a ConeThe Cone: Slant FirstRecap: Pyramid Surfaces