Question
A cube has a volume of 729 cubic centimeters. What can be concluded about the cube? Check all that apply.
Recall the formula Cube volume = s cubed.
The side length, s, can be found using the equation 3 s = 729
This is a perfect cube.
The side length is 243 centimeters.
The side length is 9 centimeters.
Taking the cube root of the volume will determine the side length.
If you multiply the volume by three, you can determine the side length.
Recall the formula Cube volume = s cubed.
The side length, s, can be found using the equation 3 s = 729
This is a perfect cube.
The side length is 243 centimeters.
The side length is 9 centimeters.
Taking the cube root of the volume will determine the side length.
If you multiply the volume by three, you can determine the side length.
Answers
GPT-4o mini
To analyze the cube with a given volume of 729 cubic centimeters, let's review the conclusions one by one based on the properties of cubes.
1. **The side length, s, can be found using the equation 3 s = 729.**
- **False**: The equation should be \(s^3 = 729\), not \(3s = 729\).
2. **This is a perfect cube.**
- **True**: 729 is a perfect cube since it can be expressed as \(9^3\).
3. **The side length is 243 centimeters.**
- **False**: The side length is not 243 cm. We'll calculate it next.
4. **The side length is 9 centimeters.**
- **True**: The cube root of 729 is \(9\) (since \(9^3 = 729\)).
5. **Taking the cube root of the volume will determine the side length.**
- **True**: Indeed, taking the cube root of the volume \(729\) gives us the side length \(s = 9\).
6. **If you multiply the volume by three, you can determine the side length.**
- **False**: Multiplying the volume by three does not provide any relation to the side length. The side length must be determined through other means, such as finding the cube root.
**Final conclusions:**
- **True:** This is a perfect cube.
- **True:** The side length is 9 centimeters.
- **True:** Taking the cube root of the volume will determine the side length.
- **False:** The side length, s, can be found using the equation \(3s = 729\).
- **False:** The side length is 243 centimeters.
- **False:** If you multiply the volume by three, you can determine the side length.
1. **The side length, s, can be found using the equation 3 s = 729.**
- **False**: The equation should be \(s^3 = 729\), not \(3s = 729\).
2. **This is a perfect cube.**
- **True**: 729 is a perfect cube since it can be expressed as \(9^3\).
3. **The side length is 243 centimeters.**
- **False**: The side length is not 243 cm. We'll calculate it next.
4. **The side length is 9 centimeters.**
- **True**: The cube root of 729 is \(9\) (since \(9^3 = 729\)).
5. **Taking the cube root of the volume will determine the side length.**
- **True**: Indeed, taking the cube root of the volume \(729\) gives us the side length \(s = 9\).
6. **If you multiply the volume by three, you can determine the side length.**
- **False**: Multiplying the volume by three does not provide any relation to the side length. The side length must be determined through other means, such as finding the cube root.
**Final conclusions:**
- **True:** This is a perfect cube.
- **True:** The side length is 9 centimeters.
- **True:** Taking the cube root of the volume will determine the side length.
- **False:** The side length, s, can be found using the equation \(3s = 729\).
- **False:** The side length is 243 centimeters.
- **False:** If you multiply the volume by three, you can determine the side length.