The volume of a sphere

How big is the Earth? Where do you start the measurements? There are no straight lines anywhere, but we can measure the circumference and calculate the radius from that. Watch the video on the circumference of a circle if you forgot how to do that. When you have the radius of a sphere, there's a formula that helps with the volume.

This is what it looks like, four-thirds times pi, times the radius cube. Plug in the radius and pi into the formula and calculate. In scientific notation, this equals 1 comma zero eight times 10 to the power of 12 cubic kilometers. It was Archimedes who came up with this, as well as with so many other things in Geometry. First, he calculated that the cylinder that exactly contains a sphere has the volume that is one and a half times larger than the volume of the sphere.

Of all the things Archimedes came up with, this was the result he was most proud of, and from here we can derive the formula for the sphere's volume. The sphere's volume is two-thirds of the cylinder's volume, and the cylinder's volume is the area of the base times the height. The area of the base is pi times the radius squared, and the height is two times the radius. We can now simplify R squared times two R is two R cubed, and two-thirds of two is four-thirds, and we're back at the formula again. The volume of a sphere equals four-thirds times pi, times the radius cubed.

This works for all spheres, a planet, a football or a scoop of ice cream.