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## 5th grade

### Course: 5th grade > Unit 11

Lesson 4: Volume word problems# Volume of rectangular prisms review

Review the basics of volume and try some practice problems.

## What is volume?

**Volume**is the amount of 3-dimensional space an object occupies. Volume is measured in cubic units.

For example, the rectangular prism below has a volume of 18 cubic units because it is made up of 18 unit cubes.

*Want to learn more about the concept of volume? Check out this video.*

## Finding volume of a rectangular prism

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.

start text, V, o, l, u, m, e, space, o, f, space, r, e, c, t, a, n, g, u, l, a, r, space, p, r, i, s, m, end text, equals start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text

*Want to learn more about finding volume of rectangular prisms? Check out this video.*

### Example 1:

start text, V, o, l, u, m, e, end text, equals, start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text

empty space, equals, 3, times, 2, times, 3

empty space, equals, 18, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

empty space, equals, 3, times, 2, times, 3

empty space, equals, 18, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

### Example 2:

start text, V, o, l, u, m, e, end text, equals, start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text

empty space, equals, 6, times, 5, times, 7

empty space, equals, 210, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

empty space, equals, 6, times, 5, times, 7

empty space, equals, 210, start text, space, c, u, b, i, c, space, u, n, i, t, s, end text

## Practice set 1: Finding volume by multiplying

*Want to try more problems like this? Check out this exercise:*Volume 1

## Practice set 2: Finding volume with unit cubes

*Want to try more problems like this? Check out these exercises:*

Volume with unit cubes 1

Volume formula intuition

## Practice set 3: Challenge items

*Want to try more problems like this? Check out these exercises:*

Decompose figures to find volume

Volume word problems

## Want to join the conversation?

- It was a breeze who else agrees.(40 votes)
- well, its different for others. we are all at different levels. <3(33 votes)

- how do you find volume with cubes(9 votes)
- you take base one and mulitiply it by the number its beside. then multiply by the height(29 votes)

- What if the width is not given.(11 votes)
- You must know, or be able to figure out the length, width, and height of s shape in the units you are using in order to calculate the approximate Volume of a rectangular solid.

If the width is not given, and no way is provided to discover the width, the volume cannot be calculated.(27 votes)

- i multiplied but i got it wrong(14 votes)
- try checking your work before you press the check button(16 votes)

- There should be like a bell when you finish(15 votes)
- I need help with practice set 3 I do not get it(13 votes)
- just to make sure when you have those weird shaped boxes then you cut them in half and add the volumes of each box to get the total volume right?(13 votes)
- STAY HOME AND STAY SAFE and i also got some right and some wrong(13 votes)
- what if the height isn't given?(3 votes)
- If the height of a rectangular prism is not given, divide the prism's volume by it's width and also divide it by it's length in order to find the height of the prism. For example:

Volume=30

Length=5

Width=3

Height=?

30/5=6, 6/3=2 so 2 equals your height.

Hope that helps.(21 votes)

- im confuson do u do 1x7x6x3=126x2 ? 🤔😠(7 votes)
- For the first problem in practice set 3, you have a shape that looks like two rectangular prisms put right next to each other. The easiest way to find the volume is the split the figure into two rectangular prisms and calculate the volume of each, and then add up those volumes to get the final volume.

If we slice the figure vertically, we can end up with a 1 x 7 x 6 rectangular prism and a 4 x 7 x 3 rectangular prism. The formula for volume is length * width * height:

V1 = 1 * 7 * 6 = 42

V2 = 4 * 7 * 3 = 84

Adding these up, our total volume is 42 + 84 = 126 cm^3(9 votes)