How to Find the Volume of Combined Shapes
Split the shape into boxes, find each volume, and add them.
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How to do it
- Split the shape into two boxes.
- Find the volume of each box.
- Add the two volumes.
Teaching tip
Try splitting the same shape a different way. Getting the same total is a good check. This sheet is aligned with Common Core 5.MD.C.5.
About this chart
An L-shaped solid split into a yellow box and a blue box, 36 + 18 = 54 cm³, and the same shape with a hidden height to find by subtracting.
What kids practice
Volume is how much space a solid shape takes up, measured by how many unit cubes fill it. Students start by counting cubes, then see that a box is made of layers: the cubes in the bottom layer times the number of layers. That leads to the formula V = length × width × height, with answers in cubic units like cm³ or ft³. Last, they find the volume of shapes made of two boxes by splitting them apart and adding.
Watch for
- Counting only the cubes you can see.
- Adding the length, width and height instead of multiplying.
- Writing square units, like cm², instead of cubic units, like cm³.
- Counting the cubes on the edges twice.
- Using the total height for the top box of a combined shape instead of finding its own height.
It's free to print, as many copies as you need. See the full volume guide for 5th grade.
More sheets in this set
- See it all
1. How to Find VolumeA unit cube and what 1 cm³ means, a 4 × 3 × 2 box counted layer by layer, and the same box with V = 4 × 3 × 2 = 24 cm³. 
2. Count the CubesBoxes built from unit cubes to count. Fewer has 4 boxes up to 3 × 3 × 3, Standard has 6 up to 5 × 4 × 4, and More has 6 that include open boxes with only some cubes inside. Includes an answer key.
3. Layer by LayerBoxes made of cubes with spaces for one layer × layers = volume. Fewer has 4 boxes with the bottom layer shaded, Standard has 6, and More has 6 that include open boxes. Includes an answer key.
4. Volume with the FormulaBoxes labeled in centimeters, inches, feet and meters to find the volume with V = length × width × height. Fewer has 4 with sides up to 6, Standard has 6 with sides up to 12, and More has 6 where some give the volume and ask for a missing side. Includes an answer key.
6. Combined ShapesSolids made of two boxes with labeled sides, to find the total volume. Fewer has 4 shapes with the two boxes in different colors, Standard has 6 with a dashed line where they split, and More has 6 with no split line and a hidden height to find. Includes an answer key.
7. Volume Word ProblemsStories about fish tanks, sandboxes, garden beds, toy chests and cereal boxes. Fewer has 3 problems, Standard has 4, and More has 5, including finding three different boxes with a volume of 24. Includes an answer key.