Geometry Calculating the Volume of Solids
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Calculating the Volume of Solids

 

 A cube is just a square that went 3D.

 

 

 
 When we have stuff in three dimensions,
 we have another measurement that we can make.
 
 The measurement is volume.
 
 Volume is the measure of how much stuff
 will fit inside the shape.
 The formula for the volume of a cube
 is length times width times height.
 

 

 
 Another way to think of this,
 is the area of the base times the height.
 

 

 
 This "area of the base" times height idea works for lots of shapes.
 Anywhere the object is the same shape on both ends
 and anywhere in between, we can use this idea.
 
 Like ...

 

 
 Objects like this are called "right" objects
 because the sides going up and down
 make right angles with the base.
 

 
 Example:
 Find the volume of a right cylinder
 with a radius of 4 and a height of 12 ...
 

 

 
 The first thing we need to do
 is find the area of the base circle.
 
 The radius is 4 ...
 
 The area of the circle is:

 Area = p 4 4

Area 5.0265

 
 We use the because we used an approximation for p
 
 The height of the cylinder is 12, so the volume is:
 

Volume = 12 base area

Volume 12 5.0265

Volume 60.318

 

   copyright 2005 Bruce Kirkpatrick

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