Volume of a Cylinder
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 12 of 62.
A cylinder is not a prism (a prism's ends are polygons), but it is built the same way: the same end all the way along. So the same idea gives its volume: the area of the end times the height. The end is a circle, and a circle's area is π times the radius squared.
This cylinder has radius 2, so its end has area pi × 2^2 = 4×pi. It is 5 high, so its volume is 4×pi × 5 = 20×pi. Leave π as a letter: 20π is the exact answer, and a decimal like 62.83 would only be close to it.
The rule is Volume of a cylinder: V = pi × r^2 × h. Square the radius first, then multiply by the height and keep π.
Challenge
Find the exact volume of the cylinder: 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