Volume of a Sphere

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Introduction: Volume of a Sphere

Well, in this instructable, I will teach you how to find the volume of a sphere. But first, the basics.

Auch in diesem instructable, ich so finden Sie die Lautst�rke der eine Kugel lernen Sie. Aber Erstens, die Grundlagen.

Eh bien, dans cette instructable, je vous enseigne comment trouver le volume d'une sph�re. Mais en premier, les notions de base.

Step 1: What the Gitmo Is a Sphere, Anyway?

A sphere (from Greek sphaira, "globe, ball,") is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the locus of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. Thus, in three dimensions, a mathematical sphere is considered to be a two-dimensional spherical surface embedded in three-dimensional space, rather than the volume contained within it (which mathematicians would instead describe as a ball). The fixed point is called the center, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.

Well, just to be simple, it is just a figure with no edged or corners, and the distance from the midpoint of the sphere to any place on the surface of the sphere is the exact same. Yes, this might seem like useless information at first, but you will need this knowledge later on.

Step 2: Finally...the Formula!

V is the volume of the sphere (or what you would usually want to get). Pi stands for the circumference of a unit circle. The radius is the distance of the midpoint to any point on the surface of the sphere, which you need to cube to get your equation. In the next equation, i will tell you how to do this backwards.

Step 3: The Equation...Backward?

Another way to do this is if you have the volume, but you need to find out the radius. You can just divide by 3/4 and divide by pi. Cool, huh?

Step 4: Now..Time for Some Problems!

Problem 1: If the radius of a sphere is 2 cm, what is the volume?

Problem 2: When the volume of a circle sphere is 32/3 pi?

Problem 3: If the radius of a given sphere is 5, what is the half the volume?

1. 32/3 pi. For this problem, you need to include the cm3, because your answer would be wrong without it. Remember, radius cubed is the number and the sign after it(if there is one).
2. 2.
3. 250/3 pi.

Step 5: Well, What Else?

1. Fill up a measuring cylinder or some other measuring instrument with water. The water should be sufficient to completely sink the sphere, but not so much that it will overflow when you submerge the sphere. Take the reading of the initial volume of water.
2. Lower your sphere slowly into the water. If your sphere is less dense than water, tie it with a thin thread to a small heavy object such as a lump of plasticine or a standard weight.
3. Take the new reading of the volume. This is the volume of the water + volume of sphere (+ volume of heavy object used to sink sphere).
4. If you tied your sphere to a heavy object, untie it, and lower just the object back into the water. Take the new reading of the volume of water + volume of heavy object.
5. Subtract either (volume of water + object + heavy weight) - (volume of water + heavy weight) OR (volume of water + object) - (volume of water). This answer is the volume of your sphere (or any object, really).

P.S. Make sure you know the volume of the cylinder beforehand; else, you might find yourself stranded! To find the volume of a cylinder, go here. Be sure to use a precise measuring cylinder, or you might get the calculations wrong!

Step 6: Another Option?

Water displacement can also be used this way.

1. Fill a graduated cylinder to the top, making sure there is no water pushing up onto the water tension. Make the calculation of the total volume, and make sure you have another water cylinder. You can also have a pitcher with a spout sticking out of a side, and having another tray or pitcher ready to hold the extruded fluid.
2. Place the object gently into the pitcher, and watch the water rise. it will rise above the peak, and then the surface tension will break when the water pours out. then, after you are sure that the water is done flowing, separate the two, and find the volume of water in the cylinder or pitcher which the water was displaced into.
3. Voila! You have your volume.

Step 7: Well...More Generally Says It.

My sources:
http://www.dkimages.com/
http://ww.fordhampprep.org/

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