The circumference of a circle is 88 cm. Using the standard value of π = 22/7, what is the area of the circle in square centimetres?

Introduction:
This problem combines properties of circles and basic algebra. You are given the circumference of a circle and asked to find its area. To solve it, you first determine the radius using the circumference formula, then use the area formula for a circle.

Given Data / Assumptions:

• Circumference of the circle (C) = 88 cm.
• Use π = 22/7 for calculations.
• We must find the area A in square centimetres.
• Standard formulas for circumference and area of a circle apply.

Concept / Approach:
The circumference of a circle is given by: C = 2 * π * r, where r is the radius. Once r is found, we use the area formula: A = π * r^2. Both formulas must use the same value of π and consistent units (centimetres here).

Step-by-Step Solution:
Step 1: Use the circumference formula C = 2 * π * r. Step 2: Substitute C = 88 and π = 22/7: 88 = 2 * (22/7) * r. Step 3: Simplify the right side: 2 * (22/7) = 44/7, so 88 = (44/7) * r. Step 4: Multiply both sides by 7: 88 * 7 = 44 * r, so 616 = 44r. Step 5: Solve for r: r = 616 / 44 = 14 cm. Step 6: Now compute the area using A = π * r^2: A = (22/7) * 14^2 = (22/7) * 196. Step 7: Calculate: 196 / 7 = 28, so A = 22 * 28 = 616 sq cm.

Verification / Alternative check:
If r = 14 cm, the circumference should be C = 2 * π * r = 2 * (22/7) * 14 = (44/7) * 14 = 44 * 2 = 88 cm, which matches the given value. This confirms that r and therefore the area calculation are correct.

Why Other Options Are Wrong:

• 308 sq cm, 154 sq cm, and 77 sq cm do not correspond to the area of a circle with radius 14 cm.
• 484 sq cm would be the area of a circle with radius sqrt(484/π), which does not match r = 14 cm and does not satisfy the given circumference.

Common Pitfalls:
Some students mistakenly use diameter instead of radius or forget to square the radius in the area formula. Others mis-handle the fraction π = 22/7, especially when simplifying expressions like (44/7) * r. Working step by step and simplifying carefully reduces such errors.

Final Answer:
The area of the circle is 616 sq cm.