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7th Grade Math / Lesson 4: Volumes: Prisms and Pyramids

What will we be learning in this lesson?

  • In this lesson you will look at how to find the volumes of objects.
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.

  • In this section we will look at the volumes of prisms and pyramids.

  • A prism is an object that has two opposing sides that are the same shape. An example is this object. It has opposing sides that are triangles. These sides are considered the bases.

  • A pyramid an object that has only one base and the sides all meet at a single point. Here the base looks like a rectangle and all of the other sides come up to meet at a point.


  • The volume of a prism is found by taking the area of one of the bases and multiplying it by the height/depth of the object.

  • Take a look at this prism.

  • If the area of the triangle base is 8 square inches and the depth is 4 inches, find the volume.

  • Volume = area of base * depth = 8 * 4 = 32 cubic inches.


  • The volume of a pyramid is 1/3 * the area of the base * the height.

  • The area of the base is 16 square cm and the height of the pyramid is 3 cm. Find the volume.

  • Volume = 1/3 * area of base * height = 1/3 * 16 * 3
                                                                = 1/3 * 48
                                                                = 16 cubic cm