Consider a cube with a volume of 64 cm3

. What can be concluded about the cube? Select the two that apply.(2 points)
Responses

The side length is 8 cm.
The side length is 8 cm.

Taking the cube root of its volume will determine its side length.
Taking the cube root of its volume will determine its side length.

The expression s2
, where s represents the side length was used to solve this problem.
The expression s squared, where s represents the side length was used to solve this problem.

The side length is 4 cm.

1 answer

To determine the properties of the cube with a volume of 64 cm³, we can analyze the provided responses:

  1. 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:
    \[ s = \sqrt[3]{64} = 4 , \text{cm} \]

  2. 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.

  3. 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.

  4. 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.