Area and volume > Volume
1234Volume

Theory

You already know that the volume of all solids that have the shape of a prism or a cylinder with base area G and height h is equal to G h .
The volume of a cuboid is therefore V ( cuboid ) = G h = l b h .
The volume of a straight cylinder is therefore V ( cylinder ) = G h = π r 2 h .

You already know that the volumeof all solids that have the shape of a pyramid or a cone with base area G and height h is equal to 1 3 G h .
The volume of a straight coneis therefore V ( cone ) = 1 3 G h = 1 3 π r 2 h .
According to Cavalieri's principle this is also true for slanting prisms, cylinders and cones, als long as h is perpendicular to the base (and top). 

The volume of a sphere is: V ( sphere ) = 4 3 π r 3 .

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