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Box Fill worksheet

Grade 6 · CCSS 6.NS.B.3

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

  1. Problem 1.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 5
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 0
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 8 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: 10 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 13 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  2. Problem 2.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 4
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 0
    • Other conductors: 3
    • Allowance per other conductor: 1.4 in³
    • Equipment grounding wires: 2
    • Largest grounding wire: 8 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: 14 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 3
    • Box volume: 18 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  3. Problem 3.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 5
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 0
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 6 AWG
    • Code edition for grounding wires: 2017 NEC or earlier
    • Devices (switches, receptacles): 2
    • Largest wire connected to the devices: 8 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 14 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  4. Problem 4.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 4
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 2
    • Other conductors: 0
    • Equipment grounding wires: 1
    • Largest grounding wire: 10 AWG
    • Code edition for grounding wires: 2017 NEC or earlier
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: Same as the largest wire in the box
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 18 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  5. Problem 5.
    • 14 AWG conductors: 1
    • 12 AWG conductors: 4
    • 10 AWG conductors: 0
    • 8 AWG conductors: 1
    • 6 AWG conductors: 0
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 6 AWG
    • Code edition for grounding wires: 2017 NEC or earlier
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: 6 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 24 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  6. Problem 6.
    • 14 AWG conductors: 1
    • 12 AWG conductors: 5
    • 10 AWG conductors: 1
    • 8 AWG conductors: 0
    • 6 AWG conductors: 0
    • Other conductors: 1
    • Allowance per other conductor: 2.2 in³
    • Equipment grounding wires: 2
    • Largest grounding wire: 12 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 2
    • Largest wire connected to the devices: 14 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 2
    • Box volume: 15 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  7. Problem 7.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 4
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 1
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 6 AWG
    • Code edition for grounding wires: 2017 NEC or earlier
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: 12 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 1
    • Box volume: 16 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  8. Problem 8.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 5
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 0
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 8 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: Same as the largest wire in the box
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 15 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  9. Problem 9.
    • 14 AWG conductors: 0
    • 12 AWG conductors: 5
    • 10 AWG conductors: 0
    • 8 AWG conductors: 0
    • 6 AWG conductors: 3
    • Other conductors: 0
    • Equipment grounding wires: 2
    • Largest grounding wire: 14 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: Same as the largest wire in the box
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 0
    • Box volume: 15 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

  10. Problem 10.
    • 14 AWG conductors: 2
    • 12 AWG conductors: 5
    • 10 AWG conductors: 1
    • 8 AWG conductors: 0
    • 6 AWG conductors: 3
    • Other conductors: 0
    • Equipment grounding wires: 3
    • Largest grounding wire: 6 AWG
    • Code edition for grounding wires: 2020 NEC or later
    • Devices (switches, receptacles): 1
    • Largest wire connected to the devices: 8 AWG
    • The box has internal cable clamps: No
    • Fixture studs or hickeys: 3
    • Box volume: 16 in³
    • Extension rings or raised covers: 0 in³

    Find: Volume required

Answer key: Box Fill worksheet

  1. 1. Volume required: 19.25 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      5×2.25=11.25 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 8 AWG allowance

      1×3=3 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×2.5=5 in³
    4. Add up every item to get the total volume the box must have

      11.25+3+5=19.25 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      13−19.25=−6.25 in³
    6. Share of the box volume used, which shows how crowded the box will be

      19.2513×100=148.08%
  2. 2. Volume required: 26.95 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      4×2.25+3×1.4=13.2 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 8 AWG allowance

      1×3=3 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×2=4 in³
    4. Fixture studs and hickeys: one allowance each at the largest wire (NEC 314.16(B)(3))

      3×2.25=6.75 in³
    5. Add up every item to get the total volume the box must have

      13.2+3+4+6.75=26.95 in³
    6. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      18−26.95=−8.95 in³
    7. Share of the box volume used, which shows how crowded the box will be

      26.9518×100=149.72%
  3. 3. Volume required: 28.25 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      5×2.25=11.25 in³
    2. Grounding wires: one allowance for all of them (NEC 314.16(B)(5), editions before 2020), at the 6 AWG allowance

      1×5=5 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×2×3=12 in³
    4. Add up every item to get the total volume the box must have

      11.25+5+12=28.25 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      14−28.25=−14.25 in³
    6. Share of the box volume used, which shows how crowded the box will be

      28.2514×100=201.79%
  4. 4. Volume required: 31.5 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      4×2.25+2×5=19 in³
    2. Grounding wires: one allowance for all of them (NEC 314.16(B)(5), editions before 2020), at the 10 AWG allowance

      1×2.5=2.5 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×5=10 in³
    4. Add up every item to get the total volume the box must have

      19+2.5+10=31.5 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      18−31.5=−13.5 in³
    6. Share of the box volume used, which shows how crowded the box will be

      31.518×100=175%
  5. 5. Volume required: 29 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      1×2+4×2.25+1×3=14 in³
    2. Grounding wires: one allowance for all of them (NEC 314.16(B)(5), editions before 2020), at the 6 AWG allowance

      1×5=5 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×5=10 in³
    4. Add up every item to get the total volume the box must have

      14+5+10=29 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      24−29=−5 in³
    6. Share of the box volume used, which shows how crowded the box will be

      2924×100=120.83%
  6. 6. Volume required: 33.2 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      1×2+5×2.25+1×2.5+1×2.2=17.95 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 12 AWG allowance

      1×2.25=2.25 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×2×2=8 in³
    4. Fixture studs and hickeys: one allowance each at the largest wire (NEC 314.16(B)(3))

      2×2.5=5 in³
    5. Add up every item to get the total volume the box must have

      17.95+2.25+8+5=33.2 in³
    6. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      15−33.2=−18.2 in³
    7. Share of the box volume used, which shows how crowded the box will be

      33.215×100=221.33%
  7. 7. Volume required: 28.5 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      4×2.25+1×5=14 in³
    2. Grounding wires: one allowance for all of them (NEC 314.16(B)(5), editions before 2020), at the 6 AWG allowance

      1×5=5 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×2.25=4.5 in³
    4. Fixture studs and hickeys: one allowance each at the largest wire (NEC 314.16(B)(3))

      1×5=5 in³
    5. Add up every item to get the total volume the box must have

      14+5+4.5+5=28.5 in³
    6. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      16−28.5=−12.5 in³
    7. Share of the box volume used, which shows how crowded the box will be

      28.516×100=178.13%
  8. 8. Volume required: 18.75 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      5×2.25=11.25 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 8 AWG allowance

      1×3=3 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×2.25=4.5 in³
    4. Add up every item to get the total volume the box must have

      11.25+3+4.5=18.75 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      15−18.75=−3.75 in³
    6. Share of the box volume used, which shows how crowded the box will be

      18.7515×100=125%
  9. 9. Volume required: 38.25 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      5×2.25+3×5=26.25 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 14 AWG allowance

      1×2=2 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×5=10 in³
    4. Add up every item to get the total volume the box must have

      26.25+2+10=38.25 in³
    5. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      15−38.25=−23.25 in³
    6. Share of the box volume used, which shows how crowded the box will be

      38.2515×100=255%
  10. 10. Volume required: 58.75 in³

    1. Conductors: each counts once at the allowance for its size (NEC 314.16(B)(1))

      2×2+5×2.25+1×2.5+3×5=32.75 in³
    2. Grounding wires: one allowance for up to four, plus a quarter for each extra (NEC 314.16(B)(5), 2020 and later), at the 6 AWG allowance

      1×5=5 in³
    3. Devices: two allowances per yoke or strap, at the largest wire connected to it (NEC 314.16(B)(4))

      2×1×3=6 in³
    4. Fixture studs and hickeys: one allowance each at the largest wire (NEC 314.16(B)(3))

      3×5=15 in³
    5. Add up every item to get the total volume the box must have

      32.75+5+6+15=58.75 in³
    6. Subtract the required volume from the space available: there is a shortfall, so the box is too small

      16−58.75=−42.75 in³
    7. Share of the box volume used, which shows how crowded the box will be

      58.7516×100=367.19%