Volume of a Sphere
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 27 of 62.
Archimedes found the sphere's volume by fitting it in a cylinder: a ball that just fits inside a can, touching the top, the bottom and the sides. The ball fills exactly two thirds of the can.
That can has radius r and height 2r, so it holds pi × r^2 × 2r = 2×pi×r^3. Two thirds of that is 4/3 × pi × r^3. For this sphere of radius 3: 4/3 × pi × 3^3 = 4/3 × pi × 27 = 36×pi.
The rule is Volume of a sphere: V = 4/3 × pi × r^3. This time the radius is cubed, because a sphere grows in all three directions at once.
Challenge
Find the exact volume of the sphere: tap it, 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