Finding the volume of a box
In 5th grade, children learn to find the volume of a box by multiplying length × width × height, and to add the volumes of two boxes joined together.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Pablo knows the area of the bottom of his toy chest. What else does he need to know to find the volume of the chest?
- Nothing more, because the area is the volume
- Its height
- The distance around its bottom
Why this matters
Length × width × height is a formula your child will carry for years: in 6th grade with fractional edges, in 8th grade with cylinders and cones, and in science. Because it is built from layers of cubes, it is a formula your child can rebuild if they forget it. It also answers practical questions, like how much water a 20 by 10 by 12 inch tank holds.
Where kids can get stuck
- Adding the three dimensions instead of multiplying, so a 4 by 3 by 2 box gets a volume of 9, not 24.
- Multiplying only two dimensions, finding the area of the base and forgetting to multiply by the height.
- Counting the overlap twice when splitting an L-shaped solid into two boxes, or using the whole shape's length for one part.
How you can help
- Measure a cereal box, shoebox, or moving box with a ruler and ask your child to find its volume. Round to whole inches to keep the arithmetic friendly, and talk about what the answer means.
- Compare two boxes from the recycling bin and ask your child to predict which holds more before measuring. Then find each volume and see if the prediction was right.
- Build an L shape from toy blocks and ask your child to find its volume by splitting it into two boxes. Ask them to try splitting it a different way and check the total matches.
For more, Bobby's Math Club has free practice at your child’s level.
Questions parents ask
Why is my child learning the volume formula this way?
Teachers connect length × width × height to layers of cubes so your child understands where it comes from. Multiplying length by width counts the cubes on the bottom layer, and multiplying by height counts the layers. A child who understands this can find volumes without relying on memory and can handle shapes built from more than one box.
What is the difference between V = l × w × h and V = b × h?
They are two ways of saying the same thing. In V = b × h, the b stands for the area of the base, which is length × width. So both formulas multiply the area of the bottom layer by the number of layers. Some problems give the area of the base directly, and the second formula fits those neatly.
How does my child find the volume of an L-shaped figure?
Your child splits the figure into two rectangular boxes, finds the volume of each with length × width × height, and adds them. For example, a box of 3 × 2 × 2 = 12 cubic units joined to one of 4 × 2 × 1 = 8 cubic units makes 20 cubic units. Checking that no part is counted twice is the key step.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited practice, completely free
- Practice that starts where your child is and grows with them
- Hints when they are stuck, and a celebration when it clicks
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.MD.C.5: “Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.MD.5)