Question

the length of the edge of a cube is 5x feet. determine the volume, in feet³, of the cube.

Explanation:

Step1: Recall the volume formula for a cube

The volume \( V \) of a cube with edge length \( s \) is given by the formula \( V = s^3 \).

Step2: Substitute the given edge length into the formula

The edge length \( s \) of the cube is \( 5x \) feet. Substituting \( s = 5x \) into the volume formula, we get:
\[
V=(5x)^3
\]

Step3: Simplify the expression

Using the exponent rule \((ab)^n=a^n\times b^n\), we have:
\[
(5x)^3 = 5^3\times x^3=125x^3
\]

Answer:

The volume of the cube is \( 125x^3 \) cubic feet.