What will be the radius of a circle (in cm) for which the circumference and the area are numerically equal?

Question

What will be the radius of a circle (in cm) for which the circumference and the area are numerically equal?

1. A. 2 (Correct answer)
2. B. 4.2
3. C. 4.5
4. D. 2.1

Correct Answer

Option A — 2

Detailed Solution & Explanation

The correct answer is 2.

Key Points

• Set the circumference and the area of the circle equal and solve for the radius r.
• Circumference = 2πr and Area = πr².
• The question says they are numerically equal:
• 2πr = πr²
• Divide both sides by πr (r ≠ 0):
• 2 = r.
• So the radius = 2 cm.
• Verification: circumference = 2π(2) = 4π; area = π(2)² = 4π — numerically equal ✓.
• 'numerically equal' means the numbers match once the common factor π cancels — the radius that makes a circle's circumference equal its area is always r = 2, independent of the units.

Exam Tip

• this is a standard one-line result worth memorising; the same technique (equate two formulas, cancel common factors) solves 'volume = surface area' type questions too.