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Decompose figures to find volume practice

Work through volume of irregular 3D figures problems that get increasingly more challenging.  The first items will have unit cubes.  Then, try some with only side-length labeled.

Decompose figures with unit cubes

Problem 1A
Unit cube:
What is the volume of the following figure?
Front ViewBack View
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
unit cubes

Problem 1B
Unit cube:
What is the volume of the following figure?
Front ViewBack View
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
unit cubes

Want to practice more problems like this? Check out this exercise.

Decompose figures with side-length labels

Problem 2B
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
cubic in

Problem 2A
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
cubic cm

Want to practice more problems like this? Check out this exercise.

Want to join the conversation?

  • mr pants purple style avatar for user Aaniyah Dominguez
    I watched the videos for all of these but I still don't get problems 2B and 2A.
    (100 votes)
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  • aqualine seed style avatar for user Vada Hutchinson
    This was not as easy as the two videos above it make it seem.
    (35 votes)
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    • mr pants green style avatar for user Ella Winnicki
      I totally agree. In the videos he does all the special colors to draw and it kinda distracts you from the actual learning of it. In the videos it looks very simple and easy, but when you are actually doing it ends up being confusing and you have many questions. At least that's how it is for me. If I was to make the videos I would try to focus from the point of view of someone who does not get the math instead of from the point of view of someone who does get it showing you it. I think that the hints are more helpful because they are made for someone who is having a little trouble with the math. The bad part is though that if you use a hint that helps you it automatically says you got it wrong, but if you watch a video that makes you more confused you get energy points for watching it.
      (60 votes)
  • mr pants teal style avatar for user Jacob Hatlas
    Is there a faster way to do the section with decomposing figures with unit cubes?
    (21 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      Yes there is a faster way, if the rectangular box-shaped pieces have a common dimension (that is, the same length, same width, or same height). For example, if the pieces have the same height, you could find the area of the base of the whole figure, by adding up areas of the rectangular bases of the pieces. Then you could multiply the area of the base of the entire figure by the height to finish the problem.
      (9 votes)
  • blobby green style avatar for user rocquemore.mariah
    Can you all start easy and if we is gitting it wright,it can start gitting harder?
    (16 votes)
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  • blobby green style avatar for user ZOE466
    I watched both videos and pay attention and still don't get 2A and 2B.
    (7 votes)
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  • blobby green style avatar for user P A R I S A :3
    Okay, so I clicked on the next practice and made sure I had finished this one and now it's making me restart the whole thing.
    (7 votes)
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  • male robot donald style avatar for user Olivia C.
    honestly all of these make no sence to me and im a 5th grader
    (6 votes)
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  • mr pants green style avatar for user Ella Winnicki
    In the videos he does all the special colors to draw and it kinda distracts you from the actual learning of it. In the videos it looks very simple and easy, but when you are actually doing it ends up being confusing and you have many questions. At least that's how it is for me. If I was to make the videos I would try to focus from the point of view of someone who does not get the math instead of from the point of view of someone who does get it showing you it. I think that the hints are more helpful because they are made for someone who is having a little trouble with the math. The bad part is though that if you use a hint that helps you it automatically says you got it wrong, but if you watch a video that makes you more confused you get energy points for watching it.
    (4 votes)
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    • winston baby style avatar for user Toneya A. Wright
      Well, I think he’s just trying to COLOR CODE. And even if he does use an abundance of different colors, it’s easy to understand what he’s talking about. And basically if you get stuck on the colors, you’re just too focused on them. He’s just trying to make it more understandable. And even if it does distract YOU. It could be easier for younger kids to understand.
      (3 votes)
  • piceratops seedling style avatar for user anthony
    In school do you think it is fun.
    (4 votes)
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  • aqualine ultimate style avatar for user 🤪
    Can you break the shape anyway you choose or you have to break the piece by what they want you to do?
    (2 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      You can break up the shape into non-overlapping pieces any way you want, as long as you correctly find the volume of each piece and correctly add up the volumes of all the pieces.
      (Note that depending on how you choose to break up the shape into pieces, you may sometimes need to perform addition and/or subtraction to find the correct dimensions of each piece.)

      Have a blessed, wonderful day!
      (6 votes)