After reading this you'll be able to Define Volume, Explain how volume is computed and find the volume of basic figures and objects in the 3 dimensional world. You will also find out about a common mistake concerning volume denominations. So, here we go: Volume refers to the total space contained within a three-dimensional figure.Volume is expressed in cubic denominations, such as cubic feet or cubic inches. [Rectangular Solid] The volume of a rectangular solid found by multiplying the Length by Width and then by the Height. You can also think of volume as taking the area of the rectangle: (L x W) and multiplying by the H. So the formula is: V = [Rectangular Solid's Width] x [Rectangular Solid's Length] x [Rectangular Solid's Height] V = L x W x H [Cube] A cube is a rectangular solid whose edges are all equal. And since all the edges are equal (L=W=H) the formula can be simplified as follows: V = [Cube's Width] x [Cube's Length] x [Cube's Height] V = L x L x L (or L in the third power) [Cylinder] A Cylinder is an object that has a circle for its base, but it also has height. To find the volume of a cylinder, use the formula below which is the area of the circle multiplied by the height of the cylinder: V = [Area of circle] x [Height of cylinder] V = (π x R x R) x H There are many useful applications of the volume formulas. Home builders may use volume to determine such things as how much concrete to purchase or how much cubic living space will be present in the completed house. Cubic living space is found by finding the total living area and then multiplying by the height of the ceilings in the house. Amount of cubic living space is important. For example, it is important to purchase an air conditioning unit that is neither too large or too small for your home. A unit that is too large will waste energy and as well as money. [Don't let this happen to you!] A very common mistake is to say that, since there are 100 centimeters in a meter, then there must be 100 cubic centimeters in a cubic meter. That's wrong! Let's see how this works: 1 liter = 1000 cm3 X (1 m3/100 cm3) = 10 m3 Since a cubic meter is the volume of a cube 1 meter on a side, and a meter is just a little more than a yard, then it should be obvious that there is no way that a liter (just a little more than a quart, remember?) is the same as TEN cubic meters! This example illustrates the dangers of trying to convert units after using an equation. As a general rule of thumb, always convert units before plugging in to an equation! Meaning of variables: V=Volume L=Length W=Width H=Height R=Radius; Length of a line segment from the center of a circle to the circle's edge. π=Pi; constant approximately equal to 3.14; used in determining the area of a circle.
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