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Geometry and Volume --- Formulas Beyond Pi

Updated on September 24, 2012
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Geometry was born as a useful tool for land measurements and lately for surveying. We probably would go back to Mesopotamia and around the Tigris River, 3,500 years ago. Little by little became what is today, especially when Euclid started to build a rigorous Science from his axioms and postulates and made his ELEMENTS, the Bible for Geometry way up until the nineteenth Century. The basic formulas that you already saw in school are represented on the graph to the right.

The three first formulas are easy to understand and keep in our memory. But lets help the kids that are new to Geometry.

axb means a multiplied by b

axa means a times a, or a squared

h which originated from the word 'height'

PI

Pi is a constant quotient that relates a circumference with its diameter; no matter how big the circle is, the diameter will increase accordingly.

The area of a circle is a result of this relationship

A=πr2,

Later, when you take calculus you will find how mathematicians came out with that formula.

ELLIPSE

If you notice an ellipse has two radius which define his oval shape. As you can see, its formula

is simple and good resemblance of an area of a circle.





VOLUME FORMULAS

If you see a CYLINDER, you can notice that is the result of adding infinitesimal circles. Remember that volume is a 'quantity' of three-dimensional space. So we will need units that resemble that space. From cm3 to m3we will find this units all over these formulas, same situation with cubic feet or cubic inches.

CYLINDER

A=πr2 H

H represent the height needed to add a third dimension to our circle area. Back in times of our first merchants, there was a need to keep track of volume. Wine, milk, beer, even grains of all kind, needed the knowledge or notion of volume.

SPHERE

The volume of an sphere might be hard to memorize but was very useful for our first astronomers from Babylonians, to Mayans to Renaissance.

V=(4/3)π r3

How to use mnemonics on this formula

Imagine both of your hands. Now left hand shows four fingers. Right hand show only three. Try playing the fitting game by interlacing your three fingers into your four left fingers. Now comes the last part: Let your sister or brother put a picture of Gordy the pig on your interlaced fingers and try to hit an stereo Cubic radio that she/ he is holding against you. Easier than this? Maybe but, now you cana see how your brain is saying geez! Mr. Cross!


ELLIPSOID

(4/3) pi r1 r2 r3

Makes sense right? You are giving an egg and they want you to find its Volume. You will need those three R's (r1,r2,r3) that define its unique volume. We still have the 4 fingers over 3 and with Gordy's picture still bothering you( pi=3.141592)



ANGLES AND MORE..by jedyteacher2007

Comments

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  • Lord De Cross profile image
    Author

    Joseph De Cross 6 years ago from New York

    That's my main goal AEVANS,

    Reaching the young in need of help. I appreciate your comments!

    LORD

  • AEvans profile image

    Julianna 6 years ago from SomeWhere Out There

    This is a great hub for both young and old. Great explanations thank you my brother! :)

  • Lord De Cross profile image
    Author

    Joseph De Cross 6 years ago from New York

    Thanks nikita! SURELY kids will find this hub

    LORD

  • nikipa profile image

    nikipa 6 years ago from Eastern Europe

    So nicely explained!

    Thank you! I am sure many people will find it useful!

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