Volume of a sphere

The volume of a sphere is $4/3\pir^3$

You may look at this and ask how am I going to remember this formula but actually, it’s quite easy to work out, it takes seconds: Just remember: Two cones = sphere:

A sphere is the same as 2 cone volumes

NOTE:

The areas shaded are all the same size (that is D=H).

We know that volume of a cone is

To measure a cone you need to multiply base and height then multiply another factor

Volume of cone = $1/3\timesπr^2\timesh$

Therefore volume of a sphere:

$(1/3\times\pir^2\timesh)+(1/3\times\pir^2\timesh)=$ Volume of a sphere

As $h = 2r$ then

$(1/3\times\pir^2\times2r)+(1/3\times\pir^2\times2r)=$ Volume of a sphere

And that’s the same as:

$(2/3\times\pir^3)+(2/3\times\pir^3)=$ Volume of a sphere

Which again is the same as:

$2(2/3\times\pir^3)=$ Volume of a sphere

$(2\times2)/3\timespir^3=$ Volume of a sphere

And

$4/3\timespir^3$ = Volume of a sphere

NOTE:

The volume of one cone must be the same volume as a hemisphere (if they have the same radius and the height of the cone is the diameter of the sphere).

Hemisphere = $1/2$ a sphere

2 cone is equal to a half sphere's volume