If a circle has radius r, the diameter is equal to which expression?

If a circle has radius r, the diameter is equal to which expression?

• A. 2r
• B. r/2
• C. r
• D. sqrt(r)

Answer: (A)

The diameter is the distance across the circle through the center, which is twice the radius. Imagine a line from the center to a point on the circle—that length is the radius, r. If you extend the same line to the opposite side of the circle, you add another radius, giving r + r = 2r. So the diameter equals 2r. The other expressions don’t match this distance: r/2 is half the radius, r is just the radius, and sqrt(r) has no direct geometric meaning for the diameter.

The diameter is the distance across the circle through the center, which is twice the radius. Imagine a line from the center to a point on the circle—that length is the radius, r. If you extend the same line to the opposite side of the circle, you add another radius, giving r + r = 2r. So the diameter equals 2r.

The other expressions don’t match this distance: r/2 is half the radius, r is just the radius, and sqrt(r) has no direct geometric meaning for the diameter.