Question

Consider a cube with a volume of 64 cm^3 what can be concluded about the cube?select the two. A. The side length is 4 cm b. Taking the cube root of its volume will determine its side length c. The side length is 8cm d. The expression s^2 where s represents the side length was used to solve this problem

Answer 1

To determine the characteristics of the cube with a volume of 64 cm³, we can analyze the provided options.

The volume \( V \) of a cube can be calculated using the formula:

\[
V = s^3
\]

where \( s \) is the length of a side of the cube. Given that \( V = 64 \) cm³, we can find the side length by taking the cube root of the volume:

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

Now let's review the options:

A. The side length is 4 cm: **True** (as we calculated).

B. Taking the cube root of its volume will determine its side length: **True** (since we used this method to find the side length).

C. The side length is 8 cm: **False** (since we've established that the side length is 4 cm).

D. The expression \( s^2 \) where \( s \) represents the side length was used to solve this problem: **False** (the volume formula uses \( s^3 \), not \( s^2 \)).

Therefore, the two correct conclusions are:

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