Question #939d5

1 Answer
Feb 8, 2018

#C = V/(pir^3)#


A geometric formula (or other constant ratio) must form a constant ratio to be consistent (and useful). Thus, the "ratio to create the rule" must be one that sets the desire ratio to some constant.

#C = V/(pir^3)#

This says that whatever the values of the volume and the radius are, this ratio will result in a constant number. Proving it to be correct would require tests on many different actual values.

One common example is the definition of the value #pi# itself! We use it in almost every geometry and trigonometry problem as a constant, but why? Where did it come from?

From a common equation we can see its derivation as the ratio (as in this problem) of the circumference of a circle to its radius:
#C = 2pir# ; #pi = C/(2r)#