Question

find the volume of the cube.
write your answer as a whole number, a proper fraction, or a mixed number.

Explanation:

Step1: Recall the volume formula for a cube

The volume formula for a cube is \( V = s^3 \), where \( s \) is the side length of the cube.

Step2: Substitute the side length into the formula

Here, \( s=\frac{7}{8}\) ft. So \( V = (\frac{7}{8})^3\).

Step3: Calculate \((\frac{7}{8})^3\)

Using the rule \((\frac{a}{b})^n=\frac{a^n}{b^n}\), we have \((\frac{7}{8})^3=\frac{7\times7\times7}{8\times8\times8}\).
\(7\times7\times7 = 343\) and \(8\times8\times8=512\). So \(V=\frac{343}{512}\) cubic feet.

Answer:

\(\frac{343}{512}\) cubic feet