What is a volume?

A volume is the amount of space that a shape can hold. 

Volume has units of length cubed because that's the number

of little element cubes that fit inside the figure.

cube = side³

rectangular prism = side1 * side2 * side3 or a b c

irregular prism = b h

cylinder = pi * radius² * height or b h = [pi] r^{2} h

pyramid = (1/3) * (base area) * height or (1/3) b h

cone = (1/3) * pi * radius² * height or (1/3) b h = 1/3 [pi] r^{2} h

sphere = (4/3) * pi * radius³ or (4/3) [pi] r^{3}

ellipsoid = (4/3) * pi * radius1 * radius2 * radius3 or (4/3) pi r₁ r₂ r₃

EXAMPLE #1

Q: It takes one man one day to dig a 2m x 2m x 2m hole. How long does it take 3 men

working at the same rate to dig a 4m x 4m x 4m hole?

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A: Let x = rate of one man = 2³ m³/ 1 day = 8m³/day

3x = rate of three men = 3(8m³/day) = 24m³/day

Volume to be shoveled = 64m³

Therefore, it would take three men

64m³/(24m³/day) = 2 2/3 days

EXAMPLE #2

Q: A rectangular sheet of wood has four small squares removed. It is then cut to

make a box that is 5cm by 4cm with a volume of 60cm³. (Four pieces of size A4 are removed.)

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A: l x h x w = 60

    h(5)(4) = 60

    h = 3

    A(1) = 4x5 = 20

    2A(2) = 2(3)(5) = 30

    2A(3) = 2(3)(4) = 24

    4A(4) = 2(3)(5) = 30

    Total A = A(1) + 2A(2) + 2A(3) + 4A(4)

    = 20 +30 +24 + 36

    =100cm² 

source:

http://www.science.co.il/Formula.asp/ (for formulas)

http://www.math.com/tables/geometry/volumes.htm (for pictures)

http://mathworld.wolfram.com/Volume.html (for formulas)

http://www.stfx.ca/special/mathproblems/grade7.html (for math problems)

http://home.blarg.net/~math/def.cgi?t=volume (for definition)

www.dictionary.com (for defintion)