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Dimensional Shapes and Surface Area | Volume Formulas | More
Volumes and Areas | Formulas Involving Angles | Pythagorean
Theorem
Volume Formulas
CA GR5 MG 1.4,
CA GR6 AF 3.2, CA GR7 MG 2.1 & 2.4
Volume is the dimension for measuring space. Volume is stated in cubic
units - cubic inches, cubic feet, cubic yards, etc. In the building trades, the
term "yards" Is often used to mean cubic yards. One cubic yard
is a quantity one yard long by one yard wide by one yard high. A
"yard" of cement would therefore be the amount of concrete that would
take up the space of one cubic yard.
Volume can be found by multiplying length times width times depth. An easier
way to picture it may be to remember that volume is surface area
multiplied by height. Volume measurements are always in cubic units. Some
common volume formulas and examples are presented below.
Volume of a cube:
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Example: |
V = s3 |
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where s
= side |
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V= (5 ft.) (5 ft.) (5 ft.) |
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V = 125 cubic feet |
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Figure 12 |
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Volume of a rectangular solid:
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Example: |
V = LWH |
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V = (10 ft.) (5ft.) (6 ft.) |
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V = 300 cubic feet |
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Figure 13 |
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Volume of a right circular cylinder:
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Example: |
V = (area of circular top) (height) or |
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V =
 r2h |
| |
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V = (3.1416)
(4 ft.) (4 ft.) (10 ft.) |
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V = 502.656 cubic feet |
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Figure 14 |
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Volume of a pyramid or cone:
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Example: |
V = |
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(area of base) (height) |
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V = |
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r2h |
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V = |
 |
(3.1416) (4) (4) (10) |
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V = |
167.552 cubic feet |
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Figure 15 |
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Example: |
V = |
 |
r3 |
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V = |
 |
(3.1416) (3 ft.) (3 ft.) (3 ft.) |
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V = |
113.0976 cubic feet or
113.10 cubic feet |
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Figure 16 |
Now, let's stop and take Practice
Exercise 9-3. (top)
For Practice Exercises on finding volumes click on this link:www.mccc.edu/~kelld/geometry3/geometry3.htm
To calculate the volume of a cube or a box automatically go to:
http://grapevine.abe.msstate.edu/~fto/tools/vol/box.html and input your values for length, height and weight and click on the
calculate button.
To calculate the volume of a cylinder automatically go to:
http://grapevine.abe.msstate.edu/~fto/tools/vol/cylinder.html and input your values for outer radius (enter 4, like in the example above),
0 for inner radius for a solid cylinder, and 10 for the height. Then click
on the calculate button to find the volume. See SELECT ANOTHER SHAPE below
the calculate button and click on this to calculate other shapes.
Next Page: More
Volumes and Areas
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