The area of a circle is 616 square centimetres. Using pi = 22/7, find the circumference of this circle in centimetres.

Introduction / Context:
This question tests the ability to move between different formulas for a circle. We are given the area and asked to find the circumference. First, we use the area formula to find the radius. Then we use the circumference formula to compute the required length. Careful substitution and simplification using pi = 22/7 will give the correct result.

Given Data / Assumptions:

• Area A = 616 sq cm.
• Area formula: A = pi * r^2.
• Circumference formula: C = 2 * pi * r.
• Use pi = 22/7.

Concept / Approach:
First solve for r from A = pi * r^2. That is, r^2 = A / pi. Then take the square root to get r. Once the radius is known, substitute into C = 2 * pi * r to find the circumference. Because pi is given as a fraction, the computation becomes a simple fraction division and multiplication exercise.

Step-by-Step Solution:
Given A = 616 sq cm.A = pi * r^2, so r^2 = A / pi = 616 / (22/7).Dividing by (22/7) is the same as multiplying by 7/22.So r^2 = 616 * (7/22).616 / 22 = 28, hence r^2 = 28 * 7 = 196.Therefore r = sqrt(196) = 14 cm.Now circumference C = 2 * pi * r = 2 * (22/7) * 14.Compute (22/7) * 14 = 22 * 2 = 44.Therefore C = 2 * 44 = 88 cm.

Verification / Alternative check:
Check the area from the found radius: pi * r^2 = (22/7) * 14^2 = (22/7) * 196 = 22 * 28 = 616 sq cm, exactly the given value. Then circumference for r = 14 is 2 * (22/7) * 14 = 88 cm. Both checks confirm that the value 88 cm is consistent.

Why Other Options Are Wrong:
44 cm is only pi * r and is half of the circumference. 22 cm and 66 cm come from errors in handling the factor of 2 or misusing the radius. 176 cm is twice the correct circumference and results from multiplying by 4 instead of 2 at some step. Only 88 cm satisfies both the area and circumference relationships simultaneously.

Common Pitfalls:
Some learners mistake radius for diameter or vice versa, leading to incorrect substitution. Others invert the fraction wrongly when dividing by pi or forget to take the square root of r^2. A clear two step process of first finding r and then calculating C helps avoid these mistakes.

Final Answer:
88 cm