Circle relation: circumference minus semidiameter equals 37 cm. If (circumference − semidiameter) = 37 cm, find the diameter of the circle (in cm).
Aptitude
Area
Difficulty: Medium
Choose an option
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A18 cm
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B12 cm
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C16 cm
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D14 cm
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ENone of these
Answer
Correct Answer: 14 cm
Explanation
Introduction / Context:This mixes a linear expression of circle measures. The “semidiameter” is the radius. We are given 2πr − r and asked to find the diameter (2r).
Given Data / Assumptions:
- Let radius = r (cm).
- Circumference C = 2πr.
- Given: C − r = 37.
Concept / Approach:Form the equation r(2π − 1) = 37 and solve for r. Use the standard approximation π = 22/7 (which makes the arithmetic exact here), then compute the diameter 2r.
Step-by-Step Solution:
2πr − r = 37 ⇒ r(2π − 1) = 37.Using π = 22/7 ⇒ 2π − 1 = 44/7 − 1 = 37/7.Then r * (37/7) = 37 ⇒ r = 37 * 7 / 37 = 7 cm.Diameter = 2r = 14 cm.Verification / Alternative check:
Check: C = 2πr = 2 * 22/7 * 7 = 44; C − r = 44 − 7 = 37 ✔Why Other Options Are Wrong:
18, 12, 16 cm do not satisfy the exact difference requirement when substituted.Common Pitfalls:
Confusing “semidiameter” with “semicircumference”. It means radius.Final Answer:
14 cm