To find the mass of 20.0 cubic feet of aluminum, we first need to convert the volume from cubic feet to cubic centimeters and then use the density to find the mass.
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Convert cubic feet to cubic centimeters:
- There are 30.48 cm in a foot, so: \[ 1 \text{ ft}^3 = (30.48 , \text{cm})^3 = 30.48^3 , \text{cm}^3 \approx 28316.8466 , \text{cm}^3 \]
- Therefore, to convert 20.0 cubic feet to cubic centimeters: \[ 20.0 , \text{ft}^3 \times 28316.8466 , \text{cm}^3/\text{ft}^3 \approx 566336.932 , \text{cm}^3 \]
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Calculate the mass using density:
- The density of aluminum is given as 2.70 g/cm³, so: \[ \text{mass} = \text{density} \times \text{volume} = 2.70 , \text{g/cm}^3 \times 566336.932 , \text{cm}^3 \] \[ \text{mass} \approx 1521063.354 , \text{g} \]
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Convert grams to kilograms:
- Since there are 1000 grams in a kilogram: \[ \text{mass in kg} = \frac{1521063.354 , \text{g}}{1000} \approx 1521.063 , \text{kg} \]
Thus, the mass of 20.0 cubic feet of aluminum is approximately 1521.1 kg when rounded to four significant figures.