The difference between the circumference of a circle and its semi-diameter is 37 cm.\n(Here, semi-diameter means the radius.)\nWhat is the diameter of the circle in cm?\n(Use pi = 22/7.)

Introduction:
This question tests understanding of circle measures and forming an equation from a word statement. The circumference of a circle is 2*pi*r. The term “semi-diameter” is another name for radius. The question says the difference between circumference and radius is 37 cm. That means (2*pi*r - r) = 37. Solving this equation gives r, and then diameter = 2r. The problem checks whether you correctly interpret “semi-diameter” and handle pi = 22/7 to get an exact integer value.

Given Data / Assumptions:

• Circumference C = 2*pi*r
• Semi-diameter = radius r
• Given: C - r = 37
• Use pi = 22/7
• Diameter d = 2r

Concept / Approach:
Translate statement into equation: 2*pi*r - r = 37. Factor r: r(2*pi - 1) = 37. Substitute pi = 22/7, solve for r, then compute diameter = 2r. This is a direct algebraic approach and avoids confusion.

Step-by-Step Solution:
2*pi*r - r = 37r(2*pi - 1) = 37Using pi = 22/7: 2*pi - 1 = 44/7 - 1 = (44 - 7)/7 = 37/7So r * (37/7) = 37r = 37 * (7/37) = 7 cmDiameter = 2r = 14 cm

Verification / Alternative Check:
With r = 7, circumference = 2*pi*r = 2*(22/7)*7 = 44 cm. Difference C - r = 44 - 7 = 37 cm, matching the condition. Therefore the diameter is 14 cm. The clean cancellation of 37 is a strong confirmation of correctness.

Why Other Options Are Wrong:
12, 16, 18, 20 cm: would imply different radii. Substituting those radii into C - r does not produce 37 cm when using pi = 22/7.

Common Pitfalls:
Interpreting semi-diameter as half of radius (incorrect).Using circumference formula pi*d but mixing d and r incorrectly.Forgetting to use pi = 22/7 consistently.Computing diameter as r instead of 2r.

Final Answer:
14 cm