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How to Use Pi to Calculate Volume of a Sphere

Updated on June 19, 2013

How to Use Pi to Find the Volume of a Ball or Sphere

Are you trying to figure out the volume of a sphere? You know you need to use Pi, and you know there's a formula for the volume of a sphere, but you need a little assistance. Let me help! Using Pi to calculate the volume of a sphere is pretty straightforward. These simple steps help you to use pi to find the volume of a ball or sphere of any size.

What Is Pi and How Do You Use It?

First, recall that Pi is a number that is used to figure out all kinds of information about circles, spheres, and cylinders. Pi is usually expressed as the decimal number 3.1415... meaning it never stops. It also never repeats! This fact has driven mathematicians insane (literally! Ever see "A Beautiful Mind?" ). Since it never actually ends, you are usually allowed to use a shortened version, like 3.14. If your teacher insists, you may have to use the Pi button on your calculator -- but never fear! just substitute it for 3.14 and you're good to go.

By the way, there are lots of on-line "math help" and tutor sites that can help you with this or any other of these concepts and steps. One good one for free math worksheets is right here.

This is a sphere (the ball, not the boy's head)


What Is a Sphere?

Of course, you do need to know what a sphere is. A sphere is simply the official name for a ball -- the Earth, a tennis ball, and a round balloon are all examples of spheres. they are all the same in shape, but not in size -- this is a key point, and it's the reason we need Pi. No matter what size your sphere is, Pi will work in an equation to find its properties -- volume, area, diameter, radius, and so on.

Let's Find the Volume!

We'll assume you know the radius of your sphere -- it's exactly half the diameter. You'll most likely be given this in the typical math problem asking for volume of a sphere with a radius of 8 inches. For example, if the diameter is 16 inches, the radius is 8 inches.

Now let's use the formula to use pi to find the volume of a ball or sphere with a radius of 8 inches. Here's the formula:

4/3 x Pi x radius cubed.

Let's break that down a little!

For this exercise, we will convert 4/3 to its decimal form: 1.33. That gives you this formula:

1.33 x Pi x radius cubed

Break it down a little more by substituting 3.14 for Pi, and we get this:

1.33 x 3.14 x radius cubed

Pop in our value for the radius, which if I remember correctly is 8 inches:

1.33 x 3.14 x 8 cubed (8x8x8)

That gives us our kind-of final product: 1.33 x 3.14 x 672

Now it's really just a matter of getting out the calculator and doing the math. When I did it, this is what I got:

1.33 x 3.14 x 672 = 2,806.4064 cubic inches



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