The Slant of a Cone
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 24 of 62.
A cone's height, its radius and its slant height make a right triangle. The height meets the radius at the centre of the base at a right angle, and the slant height is the hypotenuse.
With radius 3 and height 4, Pythagoras gives s^2 = 3^2 + 4^2 = 25, so the slant height is 5. The rule is Slant height: s^2 = r^2 + h^2. Unlike the pyramid there is no half: the radius already runs from the centre to the edge.
The rule runs backwards too. Knowing the slant height and the radius gives the height, which is what the volume needs.
Challenge
The cone's slant height is marked ?. Find it, then press Check.
Try it yourself
Find the marked part of 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