Many solids aren’t simply a polyhedral, a cone, or a cylinder. Many shapes are made up of two or more shapes or a composite solid.

Example: Determine how to find the amount of concrete needed to create a square concrete planter.

The square concrete planter is in the shape of a ___?____.

Interactive popup. Assistance may be required.

Check your answer

The inside of the square concrete planter is in the shape of a ____?____.

Interactive popup. Assistance may be required.

Check your answer

Interactive popup. Assistance may be required.

Put the smaller cube inside the larger cube.

To find the amount of cement needed to create the square planter, find the Interactive button. Assistance may be required. __________ volume of the outside and Interactive button. Assistance may be required. __________ inside cube then Interactive button. Assistance may be required. __________ subtract the Interactive button. Assistance may be required. __________ volume of the inner cube from the Interactive button. Assistance may be required. __________ outer cube.

Example: Find the volume of a "koozie." (The "koozie" is the space between a cylinder and another cylinder inside of it.)

Write an explanation of how you would find the volume of the “koozie.”

Interactive popup. Assistance may be required.

View a possible answer.

To find the volume of the koozie material find the volume of the cylinder with the koozie’s outside diameter and height minus the volume of the cylinder with the soda can’s diameter and the part of the can’s height that fits inside the koozie.

Write a conjecture for finding the volume of a figure made from one solid inside another. 

Interactive popup. Assistance may be required.

Check your answer

The volume of a figure made from one solid inside another is the difference between the outside and inside volume.

Extra Practice: Write a conjecture about the volume of composite solids.  Use the hexagonal bolt with a cylindrical shaft to explore the conjecture.

Interactive popup. Assistance may be required.

Check your answer

The total volume of a figure made by combining two solids together is the sum of the volumes of each solid.