Volume

Volume is a measurement of the amount of space that 3-d objects holds. For example, if a question on the GED math test asked you to calculate the volume of a cup, you can’t just say how many ounces it holds. You need to say how many cubes of a unit, like cubic inches, fit into the cup. For this reason volume is always represented in cubic units, such as 5 yards³.

Volume of a Cube

Volume = edge³

To find the volume of a cube, just cube the length of the edge. Cubing something just means multiplying it by itself two times. In the example above you would just multiply 5 by itself two times:

5³ = 5 x 5 x 5 = 125 in.³ (or 125 cubic inches)

Volume of a Rectangular Container

Volume = length x height x width

To find the volume of a rectangular container, multiply its length by its height by its width. If you were asked to find the volume of the above rectangular solid, just multiply 4 by 2 by 1.5.

4 x 2 = 8

8 x 1.5 = 12

volume = 12 ft.³

Volume of a Cylinder

Volume = π x radius² x height

To find the volume of a cylinder, square the radius, multiply that by the height, and multiply that by pi.

2² = 4

4 x 4 = 16

16 x π (3.14) = 50.24

v = 50.24 cm³

Volume of a Pyramid

Volume = 1/3 x (base edge)² x height

To find a square base pyramid’s volume, first square the length of one of its base sides, multiply that by its height, and multiply that number by a third (1/3).

3² = 9

9 x 5 = 45

45 x 1/3 = 15

v = 15 ft³

Volume of a Cone

Volume = 1/3 x π x radius² x height


Square the radius, multiply that by the cone’s height, multiply by pi, then multiply by 1/3.

3² = 9

9 x 7 = 63

63 x π (3.14) = 197.82

197.82 x 1/3 = 65.94

v = 65.94 cm³

 

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9 comments

  1. Zach says:

    I’m taking my GED tomorrow – the Math portion in the morning. I hope I pass. Your website has helped me a lot. Volume and everything is one of my weakest points.

  2. sandiin says:

    how do you times with the 1/3

  3. nanzina says:

    Hi and thank you for your help your site is one of the best yet its helped me so much have not passed my math test about three times now and they say that i need to stay focused more on the calculator can you help me to understand it in a simple way i feel that im burnt out from studing too muck that i cant remember the math please help me my test is at the end of april i will do my best and i will pray about it thanks for all your help… blessings to you for all your help.

  4. Krysten says:

    I have been so scared of math, and too humiliated to ask for help. I take my test tomorrow and after a couple hours on this site I am literally almost in tears.. for once math is starting to make sense.. here’s to hoping I can remember all of this tomorrow!!(:

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