Contributor: Erika Wargo. Lesson ID: 12580
Have you ever bought a box of cereal or some other substance and opened it to find it halffull? The volume of cereal doesn't match the volume of the box! Learn what volume means and how to find it!
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 in^{3}.
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 cm^{3}. If the edges of a single cube are 1 ft. long, the volume of that cube is 1 ft^{3}. 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:
Think about the questions above after watching the video:
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
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 in^{3}.
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: in^{2}, cm^{2}, ft^{2}
Volume: in^{3}, cm^{3}, ft^{3}
Example Find the volume of the cereal box with the given dimensions:

7  1  in 
2  

12  1  in 
2  

2  3  in 
4 
This problem can be solved in two ways:

7  1  in,  7  1  =  15 
2  2  2  

12  1  in,  12  1  =  25 
2  2  2  

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 

7  1  in,  7.5  in 
2  

12  1  in,  12.5  in 
2  

2  3  in,  2.75  in 
4 
7.5 x 12.5 x 2.75 = 257.8125 in^{3}
In your math journal, write a response to the following:
In the Got It? section, you will practice finding the volume of rectangular solids as you play interactive games.