Exercises: Measuring Volume by Counting Unit Cubes
Work through each section in order. Remember: volume counts every cube in a figure, including cubes hidden from view, and every answer needs the correct unit.
Warm-Up: Review What You Know
These problems review skills you have already learned.
A figure is packed with unit cubes, no gaps or overlaps: a single flat layer, 3 cubes long and 2 cubes wide (all cubes visible). Enter just the number of unit cubes.
Which measurement uses "cubic units," not "square units"?
the area of a rectangle
the volume of a box
the perimeter of a triangle
the length of a line
What is 8 × 3?
Fluency Practice
Count every unit cube in this figure, including any hidden from view. Enter just the number.
Using the layer-counting strategy, find the total number of unit cubes in this figure: one layer has 4 × 2 cubes, and there are 3 identical layers. Enter just the number.
This L-shaped figure is packed with unit cubes, no gaps or overlaps. One section is 3 cubes long, 2 cubes wide, 2 cubes tall. The other section is 2 cubes long, 1 cube wide, 2 cubes tall. Count every cube, including hidden ones, and enter the total.
This step-shaped figure is packed with unit cubes, no gaps or overlaps. The bottom section is 4 cubes long, 3 cubes wide, 1 cube tall. The top section is 2 cubes long, 3 cubes wide, 1 cube tall. Count every cube, including hidden ones, and enter the total.
This figure is built from cubes with edge length 1 centimeter, arranged 3 cubes long, 2 cubes wide, and 2 cubes tall, no gaps or overlaps. What is its volume in cubic centimeters?
This figure is built from cubes with edge length 1 inch, arranged 2 cubes long, 2 cubes wide, and 4 cubes tall, no gaps or overlaps. What is its volume in cubic inches?
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