Question

the length of the edge of a cube is 5x feet. determine the volume, in feet³, of the cube.
reference sheet
images of geometric formulas and special right triangles
the number of degrees of arc in a circle is 360.
the number of radians of arc in a circle is 2π.
the sum of the measures in degrees of the angles of a triangle is 180.
options:
15x³
25x²
25x³
125x³

Explanation:

Step1: Recall the formula for the volume of a cube

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

Step2: Substitute the given edge length into the formula

The edge length of the cube is \( 5x \) feet. So we substitute \( s = 5x \) into the volume formula:
\( V=(5x)^3 \)

Step3: Simplify the expression

Using the exponent rule \( (ab)^n=a^n\times b^n \), we have \( (5x)^3 = 5^3\times x^3 \). Since \( 5^3=125 \), this simplifies to \( 125x^3 \).

Answer:

\( 125x^3 \) (corresponding to the option with \( 125x^3 \))