The circumference of a circle is 88 cm. Using pi = 22/7, find the area of the circle in square centimetres.

Introduction / Context:
This problem connects two standard formulas for a circle: one for circumference and one for area. We are given the circumference and must find the area. To do this, we first determine the radius from the circumference and then substitute that radius into the area formula. This tests multi step reasoning with basic circle geometry.

Given Data / Assumptions:

• Circumference C = 88 cm.
• Formula for circumference: C = 2 * pi * r.
• Formula for area: A = pi * r^2.
• Use pi = 22/7 as standard approximation.

Concept / Approach:
Step one is to solve for the radius r using C = 2 * pi * r. Once r is known, step two is to compute A = pi * r^2. Because pi is given as 22/7, calculations can be simplified by using fraction arithmetic. The key is to perform operations carefully and keep track of units, ending with square centimetres for area.

Step-by-Step Solution:
Given C = 88 cm and C = 2 * pi * r.Substitute pi = 22/7: 88 = 2 * (22/7) * r.Compute 2 * (22/7) = 44/7.So 88 = (44/7) * r.Multiply both sides by 7 to clear denominator: 88 * 7 = 44 * r.Compute 88 * 7 = 616, so 616 = 44 * r.Therefore r = 616 / 44 = 14 cm.Now area A = pi * r^2 = (22/7) * 14^2.Compute 14^2 = 196, so A = (22/7) * 196.196 / 7 = 28, hence A = 22 * 28 = 616 sq cm.

Verification / Alternative check:
We can check by reversing the process. With radius r = 14 cm, circumference C should be 2 * pi * r = 2 * (22/7) * 14 = (44/7) * 14 = 44 * 2 = 88 cm, which matches the given value. The area from this radius is (22/7) * 196 = 616 sq cm, confirming that the computation is consistent at every step.

Why Other Options Are Wrong:
308 sq cm would be obtained if we mistakenly used r^2 = 98 instead of 196. 154 sq cm and 77 sq cm are fractions of the correct area and arise from missing multiplication steps. 484 sq cm might come from squaring 22 instead of using the radius properly. None of these fit both the circumference and area formulas simultaneously for a single radius value.

Common Pitfalls:
Typical errors include confusing diameter with radius, or using C = pi * r instead of 2 * pi * r. Some learners also forget to square the radius when computing the area, which halves the correct value. Careful substitution and stepwise solving, as shown, minimise these mistakes. Always verify by recomputing the circumference from the found radius.

Final Answer:
616 sq cm