Wire reshaped: A circular wire is bent to form a rhombus with side 11 cm (perimeter conserved). Find the diameter of the original circular wire.
Aptitude
Area
Difficulty: Easy
Choose an option
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A28 cm
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B3.5 cm
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C7 cm
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D14 cm
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E22 cm
Answer
Correct Answer: 14 cm
Explanation
Introduction / Context:When a wire is reshaped, length (perimeter) remains constant. We convert between a circle’s circumference and a rhombus’ perimeter.
Given Data / Assumptions:
- Rhombus side = 11 cm → Perimeter = 4 * 11 = 44 cm
- Same length becomes circle circumference
- Use π = 22/7 unless stated
Concept / Approach:Circumference C = π * d. With C known (44 cm), solve for diameter d.
Step-by-Step Solution:
C = 44 cmd = C / π = 44 / (22/7) = 44 * 7 / 22 = 14 cmVerification / Alternative check:Radius r = 7 cm. Circumference 2πr = 2 * 22/7 * 7 = 44 cm, matches the wire length.
Why Other Options Are Wrong:28 cm is twice the correct diameter; 7 cm is the radius; 3.5 cm is quarter of the diameter; 22 cm is unrelated here.
Common Pitfalls:Using 2πr formula but substituting d for r or forgetting perimeter equality during shape change.
Final Answer:14 cm