To determine the correct conclusions about the cube with a volume of \( 64 , \text{cm}^3 \), let's analyze the statements provided.
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Volume of a Cube: The formula for the volume of a cube is given by \( V = s^3 \), where \( s \) is the side length of the cube.
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Finding the Side Length: To find the side length, we take the cube root of the volume. \[ s = \sqrt[3]{V} = \sqrt[3]{64 , \text{cm}^3} = 4 , \text{cm} \]
Now we can evaluate the options:
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"The expression s², where s represents the side length was used to solve this problem." - This statement is false because the volume relates to \( s^3 \), not \( s^2 \).
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"The expression s squared, where s represents the side length was used to solve this problem." - This statement is also false for the same reason.
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"Taking the cube root of its volume will determine its side length." - This statement is true as we used the cube root to find \( s \).
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"The side length is 4 cm." - This statement is true, as we calculated \( s = 4 , \text{cm} \).
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"The side length is 8 cm." - This statement is false because, based on our calculation, the side length is not 8 cm.
Thus, the two correct conclusions from the options provided are:
- Taking the cube root of its volume will determine its side length.
- The side length is 4 cm.