Measuring Cubic Volume: Rectangular Solids

Contributor: Erika Wargo. Lesson ID: 12580

Have you ever bought a box of cereal or some other substance and opened it to find it half-full? The volume of cereal doesn't match the volume of the box! Learn what volume means and how to find it!


Measurement and Data, Solid Geometry (3D)

learning style
Auditory, Kinesthetic, Visual
personality style
Grade Level
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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  • Which of the three boxes has the greatest volume?
  • Not which box is the loudest, but which one takes up the most space?
  • What information do you need in order to figure that out?

Geometric solids are shapes that take up space.

The space occupied by a shape is called volume. To find the volume of a shape, calculate the number of unit cubes it would take to fill the object. When finding the volume, you can imagine that you are building the shape out of unit cubes of a particular size. For example, if you have a cube that has sides that are 1 inch long, the cube has a volume of 1 cubic inch or 1 in3.

The same is true if the units are centimeters, feet, or any other unit of measurement. If the edges of a single cube are 1 cm long, the volume of that cube is 1 cm3. If the edges of a single cube are 1 ft. long, the volume of that cube is 1 ft3. The 3 that comes after the unit is read as “cubic.”

Learn more about volume and visual representations of cubic units as you watch Volume with Unit Cubes (Missing Cubes), from Alex Lochoff, below. Answer the sentences below based on the information in the video:

  • The volume of a cube is found by multiplying __________ x __________ x __________.
  • What is volume?
  • What three dimensions are used to find the volume of a rectangular prism?

Think about the questions above after watching the video:

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To find the volume of a cube or box, multiply three measurements: length, width, and height. Remember, when multiplying numbers, you can multiply them in any order.

Volume = length x width x height

  • length how long it is
  • width how wide it is
  • height how tall it is

Example Find the volume of the box with a length of 21 in, width of 10 in, and height of 15 in.

When solving problems involving a formula and geometric shapes, it may be helpful to sketch the figure. Then, plug the numbers into the formula and multiply.

length: 21 in.

width: 10 in.

height: 15 in.

V = l x w x h, so V = 21 x 10 x 15

The volume is 3,150 in3.

Don’t forget to include the appropriate units when solving problems such as volume and area. Volume is measured in cubic units and area is measured in square units.

It may be helpful to remember that volume is found using three dimensions that are multiplied together, so it is named with cubic units, or an exponent of 3. Area is found using two dimensions that are multiplied together, so it is named with square units, or an exponent of 2.

Area: in2, cm2, ft2

Volume: in3, cm3, ft3

Example Find the volume of the cereal box with the given dimensions:

  • length:
7 1 in
  • height:
12 1 in
  • width:
2 3 in


This problem can be solved in two ways:

  1. Multiply mixed numbers by converting to improper fractions:
  • length:
7 1 in, 7 1 = 15
2 2 2
  • height:
12 1 in, 12 1 = 25
2 2 2
  • width:
2 3 in, 2 3 = 11
4 4 4


      15 x 25 x 11 = 4,125 , which simplifies to  257 13 in 3
2 2 4 16 16  


  1. Change the fractions to decimals and multiply:
  • length:
7 1 in, 7.5 in
  • height:
12 1 in, 12.5 in
  • width:
2 3 in, 2.75 in


7.5 x 12.5 x 2.75 = 257.8125 in3

In your math journal, write a response to the following:

  1. In your own words, what is volume?
  2. How is volume different from area?
  3. If you know the length of one side of a cube, can you figure out the volume? Explain your reasoning.

In the Got It? section, you will practice finding the volume of rectangular solids as you play interactive games.

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