Three times the circumference of a circle is numerically equal to its area. What is the diameter of the circle?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12
The circumference of a circle is \(2\pi r\) and its area is \(\pi r^2\). Setting the two given quantities equal gives the radius.
\(3\times2\pi r=\pi r^2\)
Dividing both sides by \(\pi r\) (\(r\) is not zero): \(6=r\)
Diameter \(=2r=2\times6=12\)
Why the other options are incorrect
Option (1) 6 — Incorrect. This is the radius, not the diameter.
Option (2) 10 — Incorrect. With radius 5, three times the circumference is \(30\pi\) but the area is \(25\pi\).
Option (4) 8 — Incorrect. With radius 4, three times the circumference is \(24\pi\) but the area is only \(16\pi\).