Difficulty: Easy
Correct Answer: 4 m
Explanation:
Introduction / Context:
This question involves concentric circles, which share the same centre but have different radii. The region between them is a circular ring or annulus. You are given the inner and outer circumferences and asked to find the width of the ring, which is simply the difference between the two radii. This tests your ability to relate circumference and radius.
Given Data / Assumptions:
Concept / Approach:
Use the circumference formula to find both the inner radius and the outer radius separately. Once you know both radii, subtract the inner radius from the outer radius to get the width of the ring. Because circumference is directly proportional to radius, this is straightforward when π is specified.
Step-by-Step Solution:
Inner circumference C1 = 352/7
Using C1 = 2 * π * r1 and π = 22/7
2 * (22/7) * r1 = 352/7
Multiply both sides by 7: 44 * r1 = 352
r1 = 352 / 44 = 8 m
Outer circumference C2 = 528/7
2 * (22/7) * r2 = 528/7
Multiply both sides by 7: 44 * r2 = 528
r2 = 528 / 44 = 12 m
Width of the ring = r2 - r1 = 12 - 8 = 4 m
Verification / Alternative check:
Recalculate circumferences from the radii. If r1 = 8 m, C1 = 2 * 22/7 * 8 = 352/7 m. If r2 = 12 m, C2 = 2 * 22/7 * 12 = 528/7 m. Both match the problem statement, confirming that the radii and thus the width are correct.
Why Other Options Are Wrong:
5 m, 3 m, 2 m, 6 m: Each of these values would lead to incorrect pairs of radii that do not match the given circumferences when substituted back into the formula.
Common Pitfalls:
Using the diameter instead of the radius in the circumference formula.
Mixing up inner and outer radius or subtracting in the wrong order.
Arithmetic mistakes when solving 44 * r = given circumference value.
Final Answer:
The width of the ring is 4 m
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