1/15
00:00

Learn more about this topic →

OO.1 Find the volume of composite figures made of unit cubes

Loading questions...

Go to the practice →

What is volume?

Volume is the amount of space an object takes up. It tells us how many unit cubes can fit inside a three-dimensional shape with no gaps or overlaps.

Example:
  • A cube that measures 1 unit on each side has a volume of 1 cubic unit (1 unit³).
  • A rectangular prism that is 3 units long, 2 units wide, and 4 units high has a volume of 3 × 2 × 4 = 24 cubic units.
Note

Volume is measured in cubic units because it tells us how many cubes with sides of 1 unit can fit inside a shape.

What are composite figures?

Composite figures are shapes made up of two or more smaller three-dimensional figures, such as cubes or rectangular prisms. To find their volume, we find the volume of each smaller figure and then add them together.

Example:
  • A large figure is made from two rectangular prisms joined together.
  • Prism A: 3 × 2 × 2 = 12 cubic units
  • Prism B: 2 × 2 × 2 = 8 cubic units
  • Total volume = 12 + 8 = 20 cubic units
Note

When finding the volume of composite figures, make sure the parts do not overlap. Add only the non-overlapping sections.

Finding volume using unit cubes

You can find the volume of a figure by counting how many unit cubes fill the space completely. Each cube represents one cubic unit of volume.

Example:
  • If a figure is made of 10 unit cubes, its volume is 10 cubic units.
  • If two parts have 6 cubes and 4 cubes, the total volume is 6 + 4 = 10 cubic units.
Note

Using unit cubes helps you visualize how much space a figure takes up before using formulas to calculate it.

Using formulas to find volume

The formula for finding the volume of a rectangular prism is Volume = length × width × height. You can use this formula for each part of a composite figure.

Example:
  • Part 1: 5 × 3 × 2 = 30 cubic units
  • Part 2: 2 × 3 × 3 = 18 cubic units
  • Total volume = 30 + 18 = 48 cubic units
Note

Remember to use the same unit for length, width, and height. The answer will always be in cubic units (such as cm³ or in³).

Steps for finding volume of composite figures

Follow these steps to find the volume of composite figures made of unit cubes or rectangular prisms:

Steps:
  • 1. Break the figure into smaller rectangular prisms or cubes.
  • 2. Find the volume of each smaller part using length × width × height or by counting cubes.
  • 3. Add the volumes of all parts together to get the total volume.
Note

If a shape has missing parts or cutouts, find the volume of the whole shape first and then subtract the missing part’s volume.

Checking your work

After solving, always check that your answer makes sense. The volume should match the size of the figure and be written in cubic units.

Example:
  • If your figure looks larger than one with a volume of 10 cubic units, your answer should be greater than 10 cubic units.
  • If your answer seems too small or too large, recheck your multiplication or addition.
Note

Always double-check the dimensions and units before adding or multiplying. Estimating first can help you know if your answer is reasonable.

Go to the practice →