Answer :
To solve the problem of finding the mass of an aluminum cylinder given its density and volume, we can use the formula for mass:
[tex]\[ \text{mass} = \text{density} \times \text{volume} \][/tex]
### Given Data
- Density of aluminum, \(\rho = 2.70 \times 10^3 \, \text{kg/m}^3\)
- Volume of the aluminum cylinder, \(V = 1.50 \, \text{m}^3\)
### Step-by-Step Solution
1. Identify the formula:
The formula to calculate mass is:
[tex]\[ \text{mass} = \rho \times V \][/tex]
2. Substitute the given values into the formula:
[tex]\[ \text{mass} = (2.70 \times 10^3 \, \text{kg/m}^3) \times (1.50 \, \text{m}^3) \][/tex]
3. Simplify the multiplication:
First, calculate the product of the numerical values:
[tex]\[ 2.70 \times 1.50 = 4.05 \][/tex]
Then, account for the powers of ten:
[tex]\[ 10^3 \, \text{kg/m}^3 \times \text{m}^3 = 10^3 \, \text{kg} \][/tex]
4. Combine these results:
[tex]\[ \text{mass} = 4.05 \times 10^3 \, \text{kg} \][/tex]
Alternatively, this can be written in standard notation as:
[tex]\[ \text{mass} = 4050 \, \text{kg} \][/tex]
### Conclusion
The mass of the aluminum cylinder is found to be \(4050 \, \text{kg}\).
Thus, the correct option from the given choices is:
[tex]\[ \boxed{4.05 \times 10^3 \, \text{kg}} \][/tex]
[tex]\[ \text{mass} = \text{density} \times \text{volume} \][/tex]
### Given Data
- Density of aluminum, \(\rho = 2.70 \times 10^3 \, \text{kg/m}^3\)
- Volume of the aluminum cylinder, \(V = 1.50 \, \text{m}^3\)
### Step-by-Step Solution
1. Identify the formula:
The formula to calculate mass is:
[tex]\[ \text{mass} = \rho \times V \][/tex]
2. Substitute the given values into the formula:
[tex]\[ \text{mass} = (2.70 \times 10^3 \, \text{kg/m}^3) \times (1.50 \, \text{m}^3) \][/tex]
3. Simplify the multiplication:
First, calculate the product of the numerical values:
[tex]\[ 2.70 \times 1.50 = 4.05 \][/tex]
Then, account for the powers of ten:
[tex]\[ 10^3 \, \text{kg/m}^3 \times \text{m}^3 = 10^3 \, \text{kg} \][/tex]
4. Combine these results:
[tex]\[ \text{mass} = 4.05 \times 10^3 \, \text{kg} \][/tex]
Alternatively, this can be written in standard notation as:
[tex]\[ \text{mass} = 4050 \, \text{kg} \][/tex]
### Conclusion
The mass of the aluminum cylinder is found to be \(4050 \, \text{kg}\).
Thus, the correct option from the given choices is:
[tex]\[ \boxed{4.05 \times 10^3 \, \text{kg}} \][/tex]
