# Cone vs Sphere vs Cylinder ## Volume of a Cone vs Cylinder

Let's fit a cylinder around a cone. The volume formulas for cones and cylinders are very similar:

 The volume of a cylinder is: π × r2 × h The volume of a cone is: 1 3 π × r2 × h

So the cone's volume is exactly one third ( 1 3 ) of a cylinder's volume.

(Try to imagine 3 cones fitting inside a cylinder, if you can!)

## Volume of a Sphere vs Cylinder

Now let's fit a cylinder around a sphere .

We must now make the cylinder's height 2r so the sphere fits perfectly inside. The volume of the cylinder is: π × r2 × h = 2 π × r3 The volume of the sphere is: 4 3 π × r3

So the sphere's volume is 4 3 vs 2 for the cylinder

Or more simply the sphere's volume is 2 3 of the cylinder's volume!

## The Result

And so we get this amazing thing that the volume of a cone and sphere together make a cylinder (assuming they fit each other perfectly, so h=2r): Isn't mathematics wonderful?

Question: what is the relationship between the volume of a cone and half a sphere (a hemisphere)?

## Surface Area No, it does not work for the cone.

But we do get the same relationship for the sphere and cylinder (2 3 vs 1)

And there is another interesting thing: if we remove the two ends of the cylinder then its surface area is exactly the same as the sphere: Which means that we could reshape a cylinder (of height 2r and without its ends) to fit perfectly on a sphere (of radius r): Same Area