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:
NOTE:
The areas shaded are all the same size (that is D=H).
We know that volume of a cone is
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
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