Volume Intro (Unit Cubes)

Volume is the amount of space inside a 3-D solid. We measure volume by counting how many unit cubes fit inside the figure with no gaps and no overlaps. Each unit cube has edges of 1 unit, so its volume is 1 cubic unit.

What Is a Unit Cube?

• A unit cube is a cube whose length, width, and height are all 1 unit.
• The volume of one unit cube is 1 cubic unit, written as 1 cu unit or 1 unit cubed.
• If the unit is a centimeter, one unit cube has a volume of 1 cubic centimeter.
• If the unit is an inch, one unit cube has a volume of 1 cubic inch.

Counting Cubes in a Rectangular Prism

• A rectangular prism is a box-shaped solid with 6 flat faces. The bottom face is called the base.
• Stack unit cubes inside the prism so they fill it completely with no gaps.
• The total number of unit cubes you fit inside is the volume in cubic units.
• For a 3 wide x 2 deep x 4 tall prism, count 3 x 2 = 6 cubes in the bottom layer, then 4 layers of 6 = 24 cubes total.

The Volume Formula V = l x w x h

• Counting every cube works, but multiplying is faster: V = length x width x height.
• Length and width give the area of the base (how many cubes fit in one layer).
• Multiplying by height adds one layer for each unit of height.
• Example: a prism with l = 5, w = 3, h = 2 has V = 5 x 3 x 2 = 30 cubic units.

Always Label the Cubic Unit

• Volume answers are written with cubic units because each cube has 3 dimensions.
• US customary: if edges are in inches, volume is cubic inches (cu in); if in feet, cubic feet (cu ft).
• Metric: if edges are in centimeters, volume is cubic centimeters (cu cm); if in meters, cubic meters (cu m).
• For larger volumes: 1 cubic foot = 1,728 cubic inches; 1 cubic meter = 1,000,000 cubic cm.
• If no real-world unit is given, use cubic units as the label.