The numerical value of the area of a circle is fourteen times that of the…

Concept: For a circle of radius r, Area = πr2 and Circumference = 2πr, since π is the fixed ratio between a circle's circumference and its diameter.

Application:

1. Let the radius be r. Write Area = πr2 and Circumference = 2πr.

2. Apply the given condition, Area = 14 × Circumference: πr2 = 14 × (2πr).

3. Divide both sides by πr (r ≠ 0): r = 28 units.

4. Substitute r = 28 into Circumference = 2πr = 2 × (22/7) × 28 = 176 units.

Cross-check: Area = πr2 = (22/7) × 282 = (22/7) × 784 = 2464 sq. units. And 14 × Circumference = 14 × 176 = 2464 sq. units, which matches the area — confirming r = 28 and Circumference = 176 units.

Result: The circumference of the circle is 176 units.