How to Calculate the Volume of a Sphere

Check out Bas Rutten's Liver Shot on MMA Surge: bit.ly/MMASurgeEp1
Mahalo math expert Allison Moffett shows you how to calculate the volume of a sphere.

What Is a Sphere?
---------------------------------------------------------------------

A sphere is the 3-dimensional version of a circle, like a ball or a marble. It is perfectly symmetrical; all points on the surface are exactly the same distance from the center (the measurement of this distance is the sphere's radius). It is also perfectly smooth; it has no flat edges or vertices (corners).cThe volume of a sphere is a geometrical measurement of the 3-dimensional space occupied by the sphere. For example, if you wanted to calculate the amount of water contained in a water balloon (assuming the water balloon were a perfect sphere), you would be looking for the water balloon's volume.c The formula used to calculate the volume of a sphere is V=(4/3)πr3.c

Step 1: Find the Radius of the Sphere
---------------------------------------------------------------------

Before finding the volume of a sphere, it is helpful to know the values of different parts of the volume formula.  One part of the formula is the radius of the sphere.  Just as the radius of a circle is the distance from the midpoint of the circle to the outer edge, the radius of the sphere is the distance from the center of the sphere to any point on the sphere's surface.c This is denoted r³ and it is one-third of the formula for finding the volume of a cube.c  

Step 2: Understand the Purpose of Pi
---------------------------------------------------------------------

You now know two parts of the formula to find the volume of a sphere.  The volume of a sphere is actually derived from another formula, that being the volume of cylinders.  Mathematicians have proven that the two formulas are related and based on that, they found that the formula for finding the volume of a sphere is (4/3)πr³.c

Step 3: Use the Formula for Calculating the Volume of a Sphere
---------------------------------------------------------------------

If you have a sphere with a radius of 6 inches, how much water can fill the sphere?  

1. Set the problem up like this:  V = (4/3) x π x 6³
2. Find what 6³ is equal to: 6 x 6 x 6 = 36 x 6 = 216
3. Rewrite the formula with value for 6³: V = (4/3) x π x 216
4. Multiply 4 x 216 and divide the product by 3: (216 x 4)/3 = 864/3 = 288
5. Multiply the value you got in #4 by π: V = 288π.  Since the radius was measured in inches, the volume would be 288π cubic inches.

It is acceptable to leave the value as 288π since π is an infinite number.  If you want to multiply the value out, then you would take 288 x 3.14159, which equals 904.78 rounded to two decimal places.  The volume of water that can fill a sphere with a radius of six inches is 904.78 cubic inches.
c 

Read more by visiting our page at:
mahalo.com/how-to-calculate-the-volume-of-a-sph…