Bunuel wrote:

If the radius of a circle were increased by 5 feet, the area of the circular region would increase by 65π square feet. What is the radius, in feet, before the increase?

(A) 4

(B) 8

(C) 9

(D) 13

(E) 18

Another way: use the answer choices.

Start with (C)

\(r = 9\)

Original area: \(πr^2 = 81π\)

New radius: \((9 + 5) = 14\)

New area: \(196π\)

Difference: \((196 - 81)π = 115π\)

That difference is too great by a lot -- almost twice 65π. Eliminate Answers D and E (the gap between difference of squares increases as numbers get larger, and we're adding the same constant).

Answer B, r = 8, is too close to 9. Try Answer (A)

Original \(r = 4\)

Original area = \(16π\)

New radius: \((4 + 5) = 9\)

New area: \(81π\)

Difference: \((81π - 16π) = 65π\)

That's a match.

Answer A

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"