Volume of a Pyramid
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 17 of 62.
Take a box and a pyramid with the same square base and the same height. Fill the pyramid with sand and pour it into the box: it takes exactly three pyramids to fill it. A pyramid holds one third of the prism around it.
This pyramid has a square base 6 by 6, so the base area is 6^2 = 36. The box around it would hold 36 × 4 = 144, and the pyramid holds a third of that: 1/3 × 36 × 4 = 48.
The rule is Volume of a pyramid: V = 1/3 × b^2 × h, a third of the base area times the height. The height is the dashed one inside, from the apex straight down to the centre of the base.
Challenge
Find the volume of the square pyramid: 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