Final answer:
The expression that represents the radius of the cylinder is 7x.
Step-by-step explanation:
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we are given that the volume is 49x² cubic units and the height is x units. We can substitute these values into the formula and solve for r:
49x² = πr²x
Divide both sides of the equation by πx:
49x = r²
Take the square root of both sides of the equation to solve for r:
r = √49x = 7x
Therefore, the correct expression for the radius of the cylinder is A. 2x.