Volume of a Cone
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 22 of 62.
A cone is to a cylinder what a pyramid is to a box. With the same base and the same height, a cone holds exactly a third of the cylinder.
This cone has radius 3, so its base circle has area pi × 3^2 = 9×pi. The cylinder with the same base and height 4 would hold 9×pi × 4 = 36×pi, and the cone holds a third of that: 12×pi.
The rule is Volume of a cone: V = 1/3 × pi × r^2 × h. Like the pyramid, it uses the true height, dashed inside the cone, never the slant height down its side.
Challenge
Find the exact volume of the cone: tap the solid, pick the rule, 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