Question

Consider a cube with a volume of%C2%A0 64%C2%A0cm3 . What can be concluded about the cube? Select the%C2%A0two that apply.(2 points) Responses 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%C2%A0s2 , where s represents the side length was used to solve this problem. The expression%C2%A0s squared, where s represents the side length was used to solve this problem. The side length is 4 cm. The side length is 4 cm. The side length is 8 cm.

Answer 1

To solve the problem, let's analyze the information provided about the cube with a volume of 64 cm³.

1. Find the side length: The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] where \( s \) is the side length. To find the side length, we take the cube root of the volume: \[ s = \sqrt[3]{V} = \sqrt[3]{64} = 4 \text{ cm} \]

Based on this analysis, we can conclude the following:

• Taking the cube root of its volume will determine its side length. (This is true)

• The side length is 4 cm. (This is true)

The other options relate to \( s^2 \) and state that it was used to solve the problem, which is incorrect, as we used \( s^3 \) to find the volume and \( s = \sqrt[3]{64} \) for the side length.

Thus, the two correct conclusions are:

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