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Calculate the volume of cuboids given different sets of dimensions or volume.
Mathematics
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9 stepshere are the solutions to the problems from the image:
Part 1· 6 steps
Complete the table
The formula for the volume of a cuboid is .
- Row 1:
- Given: Length , Width , Height
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 , Width , Volume
- Row 2:
Rearrange the volume formula to find height.
$$ \text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}} $$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 , Height , Volume
- Row 3:
Rearrange the volume formula to find length.
$$ \text{Length} = \frac{\text{Volume}}{\text{Width} \times \text{Height}} $$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 , Width , Height
- Row 4:
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?"
Recall the formula for the volume of a cuboid using base area.
In this context, "length" is likely referring to the missing dimension, which is the height of the cuboid, given the base area.
Substitute the given values into the formula.
Solve for the height (which the question refers to as "length").
The "length" (height) of the cuboid is .
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