The area of a circle is numerically equal to 7 times its circumference. What is the diameter of the circle?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28
Write both with the radius: area \(=\pi r^2\) and circumference \(=2\pi r\). Setting area \(=7\times\) circumference, \(\pi r\) cancels.
\(\pi r^2=7\times2\pi r\)
Dividing by \(\pi r\): \(r=14\)
Diameter \(=2\times14=28\)
Why the other options are incorrect
Option (1) 14 — Incorrect. This is the radius; the diameter is twice it.
Option (3) 7 — Incorrect. With \(d=7\), \(r=3.5\): area \(=\pi\times12.25\) but \(7\times\) circumference \(=7\times7\pi=49\pi\), not equal.
Option (4) 56 — Incorrect. With \(d=56\), \(r=28\): area \(=784\pi\) but \(7\times\) circumference \(=392\pi\), not equal.