The volume of a pyramid is the number of cubic units required to fill the solid figure. The difference between the volume of a prism and the volume of a pyramid is that the volume of a pyramid is 1 3 the volume of a prism having the same base and same height.

The formula for the volume of a pyramid is: V = 1 3 B∙h

Just like in the prism, B stands for the area of the base of the pyramid. In a pyramid, h stands for the height of the pyramid, the perpendicular distance from the base to the apex of the pyramid.

Now, let's see some examples of how to find the volume of a pyramid.

Example

Find the volume of the pyramid.

Answer the following questions. Click on the blank spaces to check your answers.

• The above pyramid is named by the Interactive popup. Assistance may be required. _______________ rectangular shape of the base.
• The formula for the area of the base is

  Interactive popup. Assistance may be required.

  _______________ .

  A = l∙ w

• The area of the base is

  Interactive popup. Assistance may be required.

  _______________ .

  A = 6 x 4 = 24 square units

• The height of the pyramid is

  Interactive popup. Assistance may be required.

  _______________ .

  8 units

• The formula for the volume of a pyramid is

  Interactive popup. Assistance may be required.

  _______________ .

  1 3 B∙h

• The volume of the pyramid is

  Interactive popup. Assistance may be required.

  _______________ .

  V = 1 3 B∙h = 1 3 (24∙8) = 1 3 (192) = 64

Source: Gizeh Pryamid, FCIT, ClipartETC

Example: Although it has deteriorated over the years, the Great Pyramid of Giza was originally 480 feet high and measured 756 feet on each side. If the average dump truck carries 18 cubic yards of material, how many dump truck loads would it take to build the Great Pyramid today?

Answer the following questions. Click on the blank spaces to check your answers.

• First, convert the measurements to yards. The answer will be in

  Interactive popup. Assistance may be required.

  _______________ .

  cubic yards

• To change 480 feet to yards Interactive popup. Assistance may be required. _______________ divide 480 feet by Interactive popup. Assistance may be required. _______________ 3 .
• There are Interactive popup. Assistance may be required. _______________ 756 ÷ 3 = 252 yards in 756 feet. (That is 2 1 2 football fields long!)
• The formula for the volume of a pyramid is Interactive popup. Assistance may be required. _______________ V = 1 3 B ∙ h .
• Find the volume by substituting the values in to the equation Interactive popup. Assistance may be required. _______________ V = 1 3 B ∙ h = 1 3 (252)² ∙ 160 = 1 3 (10,160,640) = 3,386,880 cubic yds .
• In order to find the number of dump truck loads needed to build the pyramid, Interactive popup. Assistance may be required. _______________ divide the volume by Interactive popup. Assistance may be required. _______________ 18 cubic yards per dump truck.
• It would take Interactive popup. Assistance may be required. _______________ 3,386,880 18 = 188,160 dump trucks loads of material to create a solid replica of the Great Pyramid.

Watch a video with more examples of finding the volumes of pyramids: