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Lesson 3: Decompose figures to find volume

# 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:
A unit cube is shown.
What is the volume of the following figure?
Front ViewBack View
unit cubes

Problem 1B
Unit cube:
A unit cube is shown.
What is the volume of the following figure?
Front ViewBack View
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?
A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 2 inches length by 6 inches width, and has a height of 5 inches. The second rectangular prism sits behind the first rectangular prism. It has a base that measures 8 inches length by 1 inch width and has a height of 5 inches.
start text, c, u, b, i, c, space, i, n, end text

Problem 2A
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
A figure made up of 2 rectangular prisms. The first rectangular prism has the dimensions 10 centimeters length by 6 centimeters width by 3 centimeters height. The second rectangular prism has the dimensions 4 centimeters length by 6 centimeters width by 4 centimeters height.
start text, c, u, b, i, c, space, c, m, end text

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

## Want to join the conversation?

• I watched the videos for all of these but I still don't get problems 2B and 2A.
• No, it's easy it's just that you have to split them apart and then find the height for the first one.
(1 vote)
• This was not as easy as the two videos above it make it seem.
• 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.
• Is there a faster way to do the section with decomposing figures with unit cubes?
• 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.
• Can you all start easy and if we is gitting it wright,it can start gitting harder?
• I watched both videos and pay attention and still don't get 2A and 2B.
• Basically, you have to split the shape into two rectangular prisms, then find the volume for each and solve.
• honestly all of these make no sence to me and im a 5th grader