Picture of Volume of a Sphere
In this Instructable we'll cover several ways to find the volume of a sphere - a locus of points that are equidistant to a fixed center in a 3D space.

What you're going to possibly need:
  • A Sphere
  • Distance measuring tool (ruler, caliper)
  • Calculator/Pen+Paper
  • Graduated cylinder + water
  • A brain (you're on - you've already got this...I'm not going to stress common sense all that much)
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Step 1: The Volume Formula

Picture of The Volume Formula
The volume of a sphere is (4/3)*pi*r3
  • 4/3 is a constant
  • Pi is a constant that for our purposes will = 3.14
  • r is the radius of the sphere, which is the distance from the center of the sphere to any point on that sphere's surface

Step 2: Gathering Information

Picture of Gathering Information
Luckily, the only piece of information we need is the radius of the sphere. There are several ways we can find the radius of a sphere. The more practical ways include deriving the radius from the diameter or the circumference.

You already know this, but:
  • Diameter - the longest segment that can exist within the sphere; this is 2*the radius
  • Circumference - the length of a circle projected by the sphere; this is 2*pi* the radius

You can quickly approximate the diameter of the sphere by holding a ruler against the longest part of the sphere. Match up the beginning of the ruler with your right eye closed; then take the measurement with your left eye closed. This gives you a terrible approximation, but an approximation nonetheless. After finding the diameter, simply divide it by 2 to yield the radius.

You can find the circumference most easily by taking a string or a wire and wrapping it across the longest portion of the sphere. Then measure the length of the string. After finding the circumference, divide by 2*pi to yield the radius.

Step 3: Plug'n'Play

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Once you've found the radius, it's only a matter of plugging it into the equation!

Step 4: Finished...but there's more! =O

Picture of Finished...but there's more! =O
Essentially, with a bit of common sense, it only takes the former 2 steps to find the volume of a sphere.

However, maybe some of you wonder why the volume formula is the way it is.
songkipark6 years ago
Dude, GREAT instructable! Still, more to do on your description of the Water Displacement method. You need to explain that the way to find the meniscus is to put you eye level to the flask (or in this case tube), and get the lowest point on the water. And, this method is almost always an estimate, because of the inaccuracy of the water level. That is the main reason that most math teachers don't have a tube and a sphere ready on your tests. It's pretty different with science teachers, because we(referring to me :) almost always have a flask ready, some marbles, and usually the water.
There is also a method to do this with gas, but I did not include it in my "Volume of a sphere." Otherwise, yours is pretty good, from my standpoint.
You can check mine out, here.