The volumeof eachindividualslice wouldbe givenby the productof the area of the baseand the height.
Sincethe heightfor eachslice is , the volumeof a singleslice wouldbe:
Now it followsthat the volumeof the entireprismis equalto the area of the basemultipliedby the number
of slices.If thereare slices,then:
Of course,you alreadyknowthis formulafrom prisms.But now you can use the sameidea to obtaina formula
for the volumeof a cylinder.
Sincethe heightof eachunit slice of the cylinderis , eachslice has a volumeof , or. Since
the basehas an area of , eachslice has a volumeof and:
This leadsto a postulatefor the volumeof any right cylinder.
Volumeof a RightCylinderThe volumeof a right cylinderwith radius and height
can be expressedas:Example 5