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Mail Room Math: Packing Boxes With Cubes
Pack boxes with unit cubes, then multiply the edge lengths.
Answer Key
Pack the boxes
Each box is packed with unit cubes. Each cube is 1 cubic unit. Use the layers to find the volume.
1.
Sofia packed this box with unit cubes.
Cubes in the bottom layer: 12
Number of layers: 2
Volume: 24 cubic units
2.
Which expression gives the volume of this box?
- A. 5 + 2 + 3
- B. 5 × 2
- C. 5 × 2 × 3
- D. (5 × 2) + 3
3.
Marcus packed this tall box.
Area of the base: 9 square units
Volume: 45 cubic units
4.
Kenji packed one layer of cubes in this box. The dashed lines show the top of the box.
Kenji needs 12 more cubes.
The volume of the full box is 24 cubic units.
Multiply the edge lengths
Multiply length × width × height to find each volume.
5.
A shipping box is 8 inches long, 5 inches wide, and 4 inches tall.
Volume = 160 cubic inches
6.
Match each box to its volume.
- 7 in × 3 in × 2 inC
- 6 in × 6 in × 3 inD
- 10 in × 4 in × 5 inB
- 9 in × 2 in × 4 inA
- A. 72 cubic inches
- B. 200 cubic inches
- C. 42 cubic inches
- D. 108 cubic inches
- E. 84 cubic inches
7.
A box is 5 cm long, 4 cm wide, and 3 cm tall. Circle every expression that gives its volume.
5 × 4 × 35 + 4 + 320 × 320 + 312 × 59 × 3
8.
Box A is 4 ft long, 3 ft wide, and 6 ft tall. Box B is 6 ft long, 4 ft wide, and 3 ft tall. Which is true?
- A. Box A has the greater volume.
- B. They have the same volume, 72 cubic feet.
- C. Box B has the greater volume.
- D. They have the same volume, 13 cubic feet.
Mail room problems
Use what you know about layers and edge lengths.
9.
The bottom of Ana's box has an area of 18 square inches. The box is 6 inches tall.
Volume = 108 cubic inches
10.
Jamal packs a box with 1-inch cubes. Each layer has 10 cubes. The full box holds 50 cubes.
The box is 5 inches tall.
11.
Which box holds the most 1-inch cubes?
- A. 8 in × 2 in × 3 in
- B. 6 in × 5 in × 2 in
- C. 3 in × 10 in × 2 in
- D. 4 in × 4 in × 4 in
12.
Mateo packs a box with 1-centimeter cubes and counts them layer by layer. The bottom layer has 4 rows of 5 cubes, and he stacks 3 layers. Mia finds the volume by multiplying 4 × 5 × 3. Explain why they get the same volume.
The bottom layer has 4 × 5 = 20 cubes, and 3 layers make 20 × 3 = 60 cubes. Mia's 4 × 5 × 3 is also 60, so both show a volume of 60 cubic centimeters.