What is the area of a circle with the circumference of 88 cms?

Concept: A circle's circumference and area are both governed by its radius r. The circumference formula C = 2πr relates r to the circumference, and the area formula A = πr2 relates r to the area. So finding the area from a given circumference is a two-step process: isolate r from the circumference formula, then substitute it into the area formula.

1. Application: From C = 2πr, solve for r: r = C ÷ (2π). With C = 88 cm and π ≈ 22/7, r = 88 ÷ (2 × 22/7) = 88 × 7 ÷ 44 = 14 cm.

2. Substitute r = 14 cm into A = πr2: A = (22/7) × 142 = (22/7) × 196 = 616 sq cm.

Cross-check: The area can also be written directly in terms of the circumference as A = C2 ÷ (4π). Using C = 88 and π ≈ 22/7: A = 882 ÷ (4 × 22/7) = 7744 × 7 ÷ 88 = 616 sq cm — the same result, confirming the answer.

Final answer: 616 sq cms.