We need to find the expression that represents the volume of a cylinder, given that the height of the cylinder is twice the radius of its base.
First, let \( r \) represent the radius of the base of the cylinder. According to the problem, the height \( h \) of the cylinder is twice the radius. Therefore, we can write the height as:
[tex]\[ h = 2r \][/tex]
The formula for the volume \( V \) of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
Substituting \( h = 2r \) into the volume formula, we get:
[tex]\[ V = \pi r^2 (2r) \][/tex]
Simplify the expression by multiplying the terms:
[tex]\[ V = 2 \pi r^3 \][/tex]
Hence, the expression that represents the volume of the cylinder in cubic units is:
[tex]\[ 2 \pi r^3 \][/tex]
Given the options, the one that matches this result is:
[tex]\[ \boxed{2 \pi x^3} \][/tex]
