Question
A cube has a volume of 216 cubic centimeters. What can be concluded about this cube? Check all that apply.
Recall the formula Cube volume = s cubed.
The side length, s, can be found using the equation 3 s = 216
This is a perfect cube.
The side length is 72 centimeters.
The side length is 6 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 = 216
This is a perfect cube.
The side length is 72 centimeters.
The side length is 6 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 solve for the properties of the cube with a volume of 216 cubic centimeters, we can use the formula for the volume of a cube, which is \( V = s^3 \), where \( s \) is the side length.
1. **The side length can be found using the equation \( s^3 = 216 \)**: This statement is incorrect as the correct equation is \( s^3 = 216 \).
2. **This is a perfect cube**: This statement is true. A perfect cube is a number that can be expressed as \( n^3 \) where \( n \) is an integer, and 216 is \( 6^3 \).
3. **The side length is 72 centimeters**: This statement is false because \( \sqrt[3]{216} \) is not 72.
4. **The side length is 6 centimeters**: This statement is true. \( 6^3 = 216 \), thus the side length \( s \) is 6 centimeters.
5. **Taking the cube root of the volume will determine the side length**: This statement is true. The side length can indeed be found by calculating \( \sqrt[3]{216} \), which is 6.
6. **If you multiply the volume by three, you can determine the side length**: This statement is false. Multiplying the volume by three will not yield the side length.
Based on this analysis, the conclusions that can be drawn about the cube are:
- This is a perfect cube.
- The side length is 6 centimeters.
- Taking the cube root of the volume will determine the side length.
1. **The side length can be found using the equation \( s^3 = 216 \)**: This statement is incorrect as the correct equation is \( s^3 = 216 \).
2. **This is a perfect cube**: This statement is true. A perfect cube is a number that can be expressed as \( n^3 \) where \( n \) is an integer, and 216 is \( 6^3 \).
3. **The side length is 72 centimeters**: This statement is false because \( \sqrt[3]{216} \) is not 72.
4. **The side length is 6 centimeters**: This statement is true. \( 6^3 = 216 \), thus the side length \( s \) is 6 centimeters.
5. **Taking the cube root of the volume will determine the side length**: This statement is true. The side length can indeed be found by calculating \( \sqrt[3]{216} \), which is 6.
6. **If you multiply the volume by three, you can determine the side length**: This statement is false. Multiplying the volume by three will not yield the side length.
Based on this analysis, the conclusions that can be drawn about the cube are:
- This is a perfect cube.
- The side length is 6 centimeters.
- Taking the cube root of the volume will determine the side length.