Recover circumference from area:\nIf the area of a circle is 616 cm^2, compute its circumference (in centimetres).

Difficulty: Easy

Correct Answer: 88 cm

Explanation:


Introduction / Context:
We invert area = πr^2 to find r, then compute circumference = 2πr. Integer-friendly values arise with π = 22/7.


Given Data / Assumptions:

  • Area A = 616 cm^2.
  • Use π = 22/7.


Concept / Approach:
Find r from r^2 = A/π, then compute C = 2πr.


Step-by-Step Solution:

r^2 = 616 / (22/7) = 616 * 7 / 22 = 28 * 7 = 196.r = 14 cm.C = 2 * (22/7) * 14 = 88 cm.


Verification / Alternative check:
Area from r = 14 is (22/7)*14*14 = 22*28 = 616, consistent with the input.


Why Other Options Are Wrong:
44 cm and 22 cm are too small; 176 cm is twice the correct value; 110 cm is unrelated to 2πr here.


Common Pitfalls:
Forgetting to take the positive square root for r, or mixing up diameter with radius in circumference.


Final Answer:
88 cm

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