If the radius of a circle is doubled, what happens to the diameter?

When the radius of a circle is doubled, the diameter, which is defined as twice the radius, also changes accordingly. The relationship between the radius and diameter is expressed mathematically: the diameter is equal to two times the radius (D = 2r).

If the radius is initially r, the original diameter would be 2r. When the radius is doubled, it becomes 2r. Consequently, the new diameter is calculated as follows: D = 2(2r) = 4r. Thus, the new diameter is indeed twice the original diameter, which confirms that when the radius is doubled, the diameter is also doubled.

This understanding of the relationship between radius and diameter illustrates why the diameter increases proportionally with any changes to the radius. The correct answer reflects this fundamental geometric principle.