Back MEASUREMENTLesson 4 - Page 2 Next
 Volume formula
 Cube   Rectangular Prism   Pyramid   Cylinder   Cone   Sphere side3   length  x width x height   1/3(length  x width x height)   π  x radius2  x height   1/3  x π  x radius2  x height 4/3  x π   x  radius3
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!

 Back Next