From Slant to Volume
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 25 of 62.
A cone is often described by its radius and its slant height, because those are the easy lengths to measure on a real one. The volume still needs the true height, so find it first.
This cone has radius 8 and slant height 17. Step one, the height: h^2 = 17^2 - 8^2 = 225, so h = 15. Step two, the volume: 1/3 × pi × 8^2 × 15 = 320×pi.
On the figure the height has no label. Tap it and pick Slant height to put its value in. Then the cone's volume has everything it needs.
Challenge
The cone's radius and slant height are labelled. Find its volume, 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