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Calculate the volume of cuboids given different sets of dimensions or volume.

Mathematics

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Step-by-step solution

9 steps

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Part 1· 6 steps

Complete the table

The formula for the volume of a cuboid is V=length×width×heightV = \text{length} \times \text{width} \times \text{height}.

  • Row 1:
    • Given: Length =6 m= 6 \text{ m}, Width =5 m= 5 \text{ m}, Height =2 m= 2 \text{ m}
  1. Calculate the volume.

        $$
        V = 6 \text{ m} \times 5 \text{ m} \times 2 \text{ m}
        $$
        $$
        V = 60 \text{ m}^3
        $$
    *   Missing value: $\boxed{60 \text{ m}^3}$
    
    • Row 2:
      • Given: Length =7 m= 7 \text{ m}, Width =6 m= 6 \text{ m}, Volume =270 m3= 270 \text{ m}^3
  2. Rearrange the volume formula to find height.

        $$
        \text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}}
        $$
    
  3. Substitute the values and calculate.

        $$
        \text{Height} = \frac{270 \text{ m}^3}{7 \text{ m} \times 6 \text{ m}}
        $$
        $$
        \text{Height} = \frac{270 \text{ m}^3}{42 \text{ m}^2}
        $$
        $$
        \text{Height} = \frac{45}{7} \text{ m} \approx 6.43 \text{ m}
        $$
    *   Missing value: $\boxed{\frac{45}{7} \text{ m}}$ or $\boxed{6.43 \text{ m}}$ (approximately)
    
    • Row 3:
      • Given: Width =50 cm= 50 \text{ cm}, Height =80 cm= 80 \text{ cm}, Volume =85000 cm3= 85000 \text{ cm}^3
  4. Rearrange the volume formula to find length.

        $$
        \text{Length} = \frac{\text{Volume}}{\text{Width} \times \text{Height}}
        $$
    
  5. Substitute the values and calculate.

        $$
        \text{Length} = \frac{85000 \text{ cm}^3}{50 \text{ cm} \times 80 \text{ cm}}
        $$
        $$
        \text{Length} = \frac{85000 \text{ cm}^3}{4000 \text{ cm}^2}
        $$
        $$
        \text{Length} = \frac{85}{4} \text{ cm} = 21.25 \text{ cm}
        $$
    *   Missing value: $\boxed{21.25 \text{ cm}}$
    
    • Row 4:
      • Given: Length =70 cm= 70 \text{ cm}, Width =50 cm= 50 \text{ cm}, Height =80 cm= 80 \text{ cm}
  6. Calculate the volume.

        $$
        V = 70 \text{ cm} \times 50 \text{ cm} \times 80 \text{ cm}
        $$
        $$
        V = 280000 \text{ cm}^3
        $$
    *   Missing value: $\boxed{280000 \text{ cm}^3}$
    

Part 2· 3 steps

Word Problem

The problem states: "The volume of the cuboid is 720000 cm³. If its base area is 2000 cm², what is its length?"

  1. Recall the formula for the volume of a cuboid using base area.

    Volume=Base Area×Height\text{Volume} = \text{Base Area} \times \text{Height}

    In this context, "length" is likely referring to the missing dimension, which is the height of the cuboid, given the base area.

  2. Substitute the given values into the formula.

    720000 cm3=2000 cm2×Height720000 \text{ cm}^3 = 2000 \text{ cm}^2 \times \text{Height}
  3. Solve for the height (which the question refers to as "length").

    Height=720000 cm32000 cm2\text{Height} = \frac{720000 \text{ cm}^3}{2000 \text{ cm}^2} Height=360 cm\text{Height} = 360 \text{ cm}

    The "length" (height) of the cuboid is 360 cm\boxed{360 \text{ cm}}.

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