Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.