Answer :
To determine the side length of a cube when given its volume, follow these steps:
1. Understand the relationship between volume and side length in a cube:
- The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the side length of the cube.
2. Given volume:
- In this problem, the volume \( V \) of the cube is 343 mm³.
3. Calculate the side length:
- To find the side length \( s \), we need to take the cube root of the volume. Mathematically, this is represented as:
[tex]\[ s = \sqrt[3]{V} \][/tex]
- Substitute the given volume into the equation:
[tex]\[ s = \sqrt[3]{343} \][/tex]
4. Evaluate the cube root:
- The cube root of 343 is 7.0 when rounded to one decimal place:
[tex]\[ s = 7.0 \][/tex]
5. Include the correct units:
- Since the volume was given in cubic millimeters (mm³), the side length will be in millimeters (mm).
Therefore, the side length of the cube is [tex]\( 7.0 \)[/tex] mm.
1. Understand the relationship between volume and side length in a cube:
- The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the side length of the cube.
2. Given volume:
- In this problem, the volume \( V \) of the cube is 343 mm³.
3. Calculate the side length:
- To find the side length \( s \), we need to take the cube root of the volume. Mathematically, this is represented as:
[tex]\[ s = \sqrt[3]{V} \][/tex]
- Substitute the given volume into the equation:
[tex]\[ s = \sqrt[3]{343} \][/tex]
4. Evaluate the cube root:
- The cube root of 343 is 7.0 when rounded to one decimal place:
[tex]\[ s = 7.0 \][/tex]
5. Include the correct units:
- Since the volume was given in cubic millimeters (mm³), the side length will be in millimeters (mm).
Therefore, the side length of the cube is [tex]\( 7.0 \)[/tex] mm.
