The area of a circle is 346.5 sq cm. Find its circumference (in cm), assuming pi = 22/7.

Introduction / Context:This problem connects a circle’s area to its circumference. The area formula is A = pi*r^2, and circumference is C = 2*pi*r. Since the area is known, we first solve for r by rearranging the area formula: r^2 = A/pi, then r = sqrt(r^2). After finding r, we substitute into C = 2*pi*r. The value of pi is specified as 22/7, which usually indicates the numbers were chosen to make r a clean value. The final circumference should be a reasonable size: since area is about 346.5, r will be around 10, making circumference around 60 to 70, which helps validate the result.

Given Data / Assumptions:

• Area A = 346.5 sq cm
• pi = 22/7
• A = pi*r^2
• C = 2*pi*r

Concept / Approach:Solve for r from A = pi*r^2, then compute circumference using C = 2*pi*r. Keep all units in cm and sq cm consistently.

Step-by-Step Solution: r^2 = A / pi = 346.5 / (22/7) = 346.5 * 7 / 22 346.5 / 22 = 15.75, so r^2 = 15.75 * 7 = 110.25 r = sqrt(110.25) = 10.5 cm C = 2*pi*r = 2*(22/7)*10.5 (22/7)*10.5 = 22*1.5 = 33 C = 2*33 = 66 cm

Verification / Alternative check:Check area using r=10.5: A = (22/7)*10.5^2 = (22/7)*110.25 = 22*15.75 = 346.5 sq cm, exactly matching the given area. So the circumference computed from this r is consistent.

Why Other Options Are Wrong: 38 is too small for a circle with this area. 76 and 88 would require a larger r, which would increase area beyond 346.5. 132 is exactly double of 66 and can come from mistakenly doubling twice.

Common Pitfalls:Using diameter instead of radius in formulas, forgetting to take square root after finding r^2, or mixing pi approximations inconsistently.

Final Answer:The circumference is 66 cm.