Cube
Rectangular Prism
Pyramid
Cylinder
Cone
Sphere 
side^{3
}length x width x height
1/3(length x width x height)
π
x radius^{2} x height
1/3 x
π
x radius^{2} x height
4/3 x
π
x radius^{3} 


Simple polygons like cubes, rectangles, and
prisms are easy to determine the volume by measuring the sides and height of
the object as noted in the chart titled “Volume formula.” These are simple
polygons; more advanced polygons are not that simple.
In the same “Volume formula” chart,
notice the symbol “
π
“ or pi for the
cylinder, cone, and sphere. The one thing in common with these shapes is
the presence of a circle. By definition, pi is the ratio of the
circumference of a circle to the circle's diameter. Pi is
always the same number, no matter which circle you use to compute it. Pi
is an infinite decimal that continues forever without repeating itself
(3.1415……). This makes pi a very weird number. The constant is named " π "
because it is the first letter of the Greek words περιφέρεια 'periphery'
and περίμετρος 'perimeter', i.e.
'circumference'.
How are irregularly shaped objects calculated? Curved
shapes require formulas from integral calculus. Integral calculus
studies the accumulation of infinitely small quantities summing to areas
under a curve, linear distance traveled, or volume displaced. But first we
need to learn the simple ones! 