Question

The volume of a cube is 27 cubic inches. Which expression represents s, the length of a side of the cube?

Recall the formula Cube volume = s cubed.
s = RootIndex 3 StartRoot 27 EndRoot
s = 3 + 3 + 3
s = StartRoot 27 EndRoot
s = 3 times 3 times 3 times 3

Answer 1

To find the length of a side of the cube \( s \) given that the volume of the cube is 27 cubic inches, we can use the formula for the volume of a cube:

\[
\text{Volume} = s^3
\]

Since we know the volume is 27, we can set up the equation:

\[
s^3 = 27
\]

To solve for \( s \), we need to take the cube root of both sides:

\[
s = \sqrt[3]{27}
\]

Knowing that \( 27 \) is equal to \( 3^3 \), we can simplify it:

\[
s = \sqrt[3]{3^3} = 3
\]

Now, evaluating the options given:

1. \( s = \sqrt[3]{27} \) - This is correct.
2. \( s = 3 + 3 + 3 \) - This is incorrect (that equals 9).
3. \( s = \sqrt{27} \) - This is incorrect (that equals \( 3\sqrt{3} \)).
4. \( s = 3 \times 3 \times 3 \times 3 \) - This is incorrect (that equals 81).

Therefore, the correct expression that represents \( s \) is:

\[
s = \sqrt[3]{27}
\]