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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Comments

  • Zach

    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.

    • Ziyi

      Good luck, Zack! I’m sure you’ll do great!

      • Juan

        Hey, how did you do? did you pass? and if so, can you give me some pointers? you can email me at floridarico2012@gmail.com

    • Megan Trotter

      did you pass your test?

      • Paul

        I don’t think the person did..otherwise I would imagine they would’ve responded..
        I’m taking mine on the 13th or 14th of this month…I missed it by a point…
        There’s one question about a birdhouse..it gives you the dimensions minus the hole for the front and at the end asks you to find out how big a piece of wood you’d need to cut out all the shapes..in approximate not around

  • sandiin

    how do you times with the 1/3

    • Ziyi

      Check here to see how to multiply fractions:

      http://www.math4ged.com/multiplying-and-dividing-fractions/

      Also, you can use the calculator that is issued to you during the test to multiply fractions.

      A third thing you could do is just to use .33 instead of 1/3. This won’t give you an exact answer, but since the test is mostly multiple choice just choose the closest one and you’ll get it right.

  • nanzina

    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.

  • Krysten

    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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