To determine the mass of 20.0 cubic feet of aluminum whose density is \(2.70 , \text{g/cm}^3\), we first need to convert cubic feet to cubic centimeters since the density is given in grams per cubic centimeter.
1 cubic foot is equivalent to \(28,316.8 , \text{cm}^3\).
So, we can convert 20.0 cubic feet to cubic centimeters:
\[ 20.0 , \text{ft}^3 \times 28,316.8 , \text{cm}^3/\text{ft}^3 = 566,336 , \text{cm}^3 \]
Now we can find the mass using the density formula:
\[ \text{mass} = \text{density} \times \text{volume} \]
Given that the density of aluminum is \(2.70 , \text{g/cm}^3\):
\[ \text{mass} = 2.70 , \text{g/cm}^3 \times 566,336 , \text{cm}^3 \]
Calculating the mass:
\[ \text{mass} = 2.70 \times 566,336 = 1,529,075.2 , \text{g} \]
Now convert grams to kilograms:
\[ \text{mass in kg} = \frac{1,529,075.2 , \text{g}}{1000} = 1,529.0752 , \text{kg} \]
Thus, the mass of 20.0 cubic feet of aluminum is approximately:
\[ \boxed{1,529.1} , \text{kg} \]