Volume of a Prism
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 8 of 62.
A cuboid's volume is the area of its end times its length: one layer, repeated. That works for every right prism, because every slice of a prism is the same shape as its end.
This prism's end is a right triangle with legs 4 and 3, so its area is 1/2 × 4 × 3 = 6. The prism is 6 long, so the volume is 6 × 6 = 36. The 5 is the triangle's slanted side. It does not change the area, so the volume does not use it.
The rule is Volume of a prism: V = 1/2 × b × h × l, the triangle's area times the length. Here b and h are the base and height of the triangle end, and l is the length of the prism.
Challenge
The prism's ends are right triangles. Find its volume: 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