Recover circumference from area: If the area of a circle is 616 cm^2, compute its circumference (in centimetres).
Aptitude
Area
Difficulty: Easy
Choose an option
-
A44 cm
-
B88 cm
-
C22 cm
-
D176 cm
-
E110 cm
Answer
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