Consider a cube with a volume of 64 cm3

To determine the side length of a cube given its volume, you can use the formula for the volume of a cube:

\[ V = s^3 \]

where \( V \) is the volume and \( s \) is the side length.

Given that the volume of the cube is 64 cm³, you can find the side length \( s \) by taking the cube root of the volume:

\[ s = \sqrt[3]{V} = \sqrt[3]{64} = 4 , \text{cm} \]

Now, let's evaluate the options given:

1. The side length is 8 cm. - False (The side length is 4 cm, not 8 cm.)
2. Taking the cube root of its volume will determine its side length. - True (The side length is determined by taking the cube root of the volume.)
3. The expression \( s^2 \), where \( s \) represents the side length was used to solve this problem. - False (The volume would use \( s^3 \), not \( s^2 \).)
4. The side length is 4 cm. - True (The side length is indeed 4 cm.)

Therefore, the two correct conclusions are:

• Taking the cube root of its volume will determine its side length.
• The side length is 4 cm.