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Circle relation: circumference minus semidiameter equals 37 cm.\nIf (circumference − semidiameter) = 37 cm, find the diameter of the circle (in cm).

Difficulty: Medium

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
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