Sphere in a Cylinder
Part of the Surface Area & Volume section of Coddy's Geometry journey. Lesson 28 of 60.
Archimedes was so proud of the sphere in the cylinder that he asked for it to be carved on his tomb. The sphere's radius r is also the can's radius, and the can's height is 2r, the sphere's diameter.
Here the ball has radius 6 and holds 288π. The can it fits in has radius 6 and height 12, so it holds 432π. Divide: 288 out of 432 is exactly two thirds.
Use the cylinder as a check whenever you work out a sphere: the sphere should always come to two thirds of its can.
Challenge
The ball fits exactly in the can: they share a radius, and the can is as tall as the ball is wide. Find the volume of each, then press Check.
Try it yourself
Find the marked part of the figure
All lessons in Surface Area & Volume
1Volume of Prisms
Volume of a CuboidDouble Every EdgeVolume of a PrismAny Triangle EndA Missing EdgeRecap: Prism Volume4Pyramids
Volume of a PyramidThe Slant HeightHeight From the SlantHeight From the VolumeRecap: Pyramids3Cylinders
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