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Dimensional Weight worksheet

Grades 5–6 · CCSS 5.MD.C.5.b

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Units: Centimeters and kilograms
- Length: 62 cm
- Width: 38 cm
- Height: 26 cm
- Actual weight: 6 kg
- Dimensional divisor: 5,000 cm³/kg
- Round weights up to: Next whole pound or kilogram
Find: Billable weight
Answer
2.
Problem 2.
- Units: Inches and pounds
- Length: 19 in
- Width: 17 in
- Height: 14 in
- Actual weight: 13 lb
- Dimensional divisor: 110 in³/lb
- Round weights up to: Next half pound or kilogram
Find: Billable weight
Answer
3.
Problem 3.
- Units: Centimeters and kilograms
- Length: 36 cm
- Width: 42 cm
- Height: 36 cm
- Actual weight: 10 kg
- Dimensional divisor: 4,250 cm³/kg
- Round weights up to: Next whole pound or kilogram
Find: Billable weight
Answer
4.
Problem 4.
- Units: Centimeters and kilograms
- Length: 50 cm
- Width: 42 cm
- Height: 24 cm
- Actual weight: 8 kg
- Dimensional divisor: 5,800 cm³/kg
- Round weights up to: Next half pound or kilogram
Find: Billable weight
Answer
5.
Problem 5.
- Units: Inches and pounds
- Length: 16 in
- Width: 10 in
- Height: 13 in
- Actual weight: 14 lb
- Dimensional divisor: 180 in³/lb
- Round weights up to: No rounding
Find: Billable weight
Answer
6.
Problem 6.
- Units: Inches and pounds
- Length: 18 in
- Width: 13 in
- Height: 13 in
- Actual weight: 13 lb
- Dimensional divisor: 180 in³/lb
- Round weights up to: Next whole pound or kilogram
Find: Billable weight
Answer
7.
Problem 7.
- Units: Centimeters and kilograms
- Length: 36 cm
- Width: 44 cm
- Height: 20 cm
- Actual weight: 5 kg
- Dimensional divisor: 5,500 cm³/kg
- Round weights up to: No rounding
Find: Billable weight
Answer
8.
Problem 8.
- Units: Centimeters and kilograms
- Length: 45 cm
- Width: 28 cm
- Height: 22 cm
- Actual weight: 7 kg
- Dimensional divisor: 5,000 cm³/kg
- Round weights up to: Next half pound or kilogram
Find: Billable weight
Answer
9.
Problem 9.
- Units: Centimeters and kilograms
- Length: 38 cm
- Width: 32 cm
- Height: 26 cm
- Actual weight: 6 kg
- Dimensional divisor: 4,500 cm³/kg
- Round weights up to: Next whole pound or kilogram
Find: Billable weight
Answer
10.
Problem 10.
- Units: Centimeters and kilograms
- Length: 45 cm
- Width: 37 cm
- Height: 34 cm
- Actual weight: 5 kg
- Dimensional divisor: 4,800 cm³/kg
- Round weights up to: Next whole pound or kilogram
Find: Billable weight
Answer

Answer key: Dimensional Weight worksheet

1. Billable weight: 13 kg
1. Find the package's volume: length × width × height
  $62 \times 38 \times 26$ $= 61,256 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{61,256}{5,000}$ $= 12.2512 kg$
3. Round both weights up to the next whole kilogram, the way carriers bill
  $dimensional 13 kg, actual 6 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(13, 6) = 13 kg$
2. Billable weight: 41.5 lb
1. Find the package's volume: length × width × height
  $19 \times 17 \times 14$ $= 4,522 in³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{4,522}{110}$ $= 41.109091 lb$
3. Round both weights up to the next half pound, the way carriers bill
  $dimensional 41.5 lb, actual 13 lb$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(41.5, 13) = 41.5 lb$
3. Billable weight: 13 kg
1. Find the package's volume: length × width × height
  $36 \times 42 \times 36$ $= 54,432 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{54,432}{4,250}$ $= 12.807529 kg$
3. Round both weights up to the next whole kilogram, the way carriers bill
  $dimensional 13 kg, actual 10 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(13, 10) = 13 kg$
4. Billable weight: 9 kg
1. Find the package's volume: length × width × height
  $50 \times 42 \times 24$ $= 50,400 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{50,400}{5,800}$ $= 8.689655 kg$
3. Round both weights up to the next half kilogram, the way carriers bill
  $dimensional 9 kg, actual 8 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(9, 8) = 9 kg$
5. Billable weight: 14 lb
1. Find the package's volume: length × width × height
  $16 \times 10 \times 13$ $= 2,080 in³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{2,080}{180}$ $= 11.555556 lb$
3. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(11.555556, 14) = 14 lb$
6. Billable weight: 17 lb
1. Find the package's volume: length × width × height
  $18 \times 13 \times 13$ $= 3,042 in³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{3,042}{180}$ $= 16.9 lb$
3. Round both weights up to the next whole pound, the way carriers bill
  $dimensional 17 lb, actual 13 lb$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(17, 13) = 17 lb$
7. Billable weight: 5.76 kg
1. Find the package's volume: length × width × height
  $36 \times 44 \times 20$ $= 31,680 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{31,680}{5,500}$ $= 5.76 kg$
3. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(5.76, 5) = 5.76 kg$
8. Billable weight: 7 kg
1. Find the package's volume: length × width × height
  $45 \times 28 \times 22$ $= 27,720 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{27,720}{5,000}$ $= 5.544 kg$
3. Round both weights up to the next half kilogram, the way carriers bill
  $dimensional 6 kg, actual 7 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(6, 7) = 7 kg$
9. Billable weight: 8 kg
1. Find the package's volume: length × width × height
  $38 \times 32 \times 26$ $= 31,616 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{31,616}{4,500}$ $= 7.025778 kg$
3. Round both weights up to the next whole kilogram, the way carriers bill
  $dimensional 8 kg, actual 6 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(8, 6) = 8 kg$
10. Billable weight: 12 kg
1. Find the package's volume: length × width × height
  $45 \times 37 \times 34$ $= 56,610 cm³$
2. Find the dimensional weight: divide the volume by the carrier's divisor, the space it counts as one unit of weight
  $\frac{56,610}{4,800}$ $= 11.79375 kg$
3. Round both weights up to the next whole kilogram, the way carriers bill
  $dimensional 12 kg, actual 5 kg$
4. The carrier charges for whichever is greater, the dimensional or the actual weight. That's the billable weight
  $max(12, 5) = 12 kg$