To determine the properties of the cube with a volume of 64 cm³, we can analyze the provided responses:
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The side length is 8 cm. - This is true because the volume \( V \) of a cube is calculated using the formula \( V = s^3 \) (where \( s \) is the side length). Since the volume is 64 cm³, we find the side length by calculating the cube root of 64:
\[ s = \sqrt[3]{64} = 4 , \text{cm} \] -
Taking the cube root of its volume will determine its side length. - This is also true. To find the side length of the cube, we take the cube root of its volume, which confirms that the side length is 4 cm.
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The expression \( s^2 \), where \( s \) represents the side length was used to solve this problem. - This is not applicable here since we used \( s^3 \) to find the volume and took the cube root to find the side length.
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The side length is 4 cm. - This is true, as we derived above.
Thus, the two correct conclusions that can be drawn about the cube are:
- The side length is 4 cm.
- Taking the cube root of its volume will determine its side length.