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7th Grade Math / Lesson 3: Volumes

What will we be learning in this lesson?

  • In this lesson you will look at how to find the area of a composite shape.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • The volume of an object is the space inside of the object.

  • Area and volume both refer to the space inside of an object. The difference is that area talks about the space inside of a flat shape. Like the following shapes:

  • To find the volume, the shape needs another dimension to it so that it is not a flat shape. Like these:

  • The volume is the amount of space inside of the shape/object.


  • To find the volume of a basic box-shaped object you need to find the area of one side of the box, this will be called the base. Then take that area and multiply it by the height of the object.

  • Take a look at this box.

  • The bottom of the box is a rectangle with side lengths of 4 and 2. So the area of the bottom (base) is 4 * 2 = 8.
  • The height of the box is 3 in. So take the area of the bottom and multiply by 3.
    8 * 3 = 24
  • The volume of this object is 24 cubic inches.


  • Find the volume of this object.

  • Follow what we did on the previous example. Take the dimensions of the bottom, 14 and 2, and multiply them together. 14 * 2 = 28. Now take the 28 and multiply by the height.
    28 * 5 = 140.

  • So the volume of this object is 140 cubic cm.

  • Can you find the volume of a 3-dimensional shape?
  • Go back to the classroom to get to your homework and any other items you need to attend to.