To determine the mass of 20.0 cubic feet of aluminum with a density of 2.70 g/cm³, we can follow these steps:
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Convert cubic feet to cubic centimeters: The conversion factor is: \[ 1 \text{ cubic foot} = 28,316.8 \text{ cubic centimeters} \] Therefore, for 20.0 cubic feet: \[ 20.0 \text{ ft}^3 \times 28,316.8 \text{ cm}^3/\text{ft}^3 = 566,336 \text{ cm}^3 \]
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Calculate the mass: We use the formula: \[ \text{mass} = \text{density} \times \text{volume} \] Given the density of aluminum is \(2.70 \text{ g/cm}^3\): \[ \text{mass} = 2.70 \text{ g/cm}^3 \times 566,336 \text{ cm}^3 = 1,528,999.2 \text{ g} \]
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Convert grams to kilograms: Since \(1 \text{ kg} = 1000 \text{ g}\): \[ \text{mass} = \frac{1,528,999.2 \text{ g}}{1000} = 1,528.9992 \text{ kg} \]
Therefore, the mass of 20.0 cubic feet of aluminum is approximately 1,529 kg.