For a circle, the difference between its circumference and its radius is 37 cm. Find the area of the circle (use π = 22/7).

Introduction / Context:This is a mixed-formula circle problem: you are given a linear relation between circumference and radius, and asked for area. The trick is to solve for the radius using the circumference formula and then compute the area using r. Taking π = 22/7 simplifies arithmetic neatly.

Given Data / Assumptions:

• Circumference C = 2πr
• C − r = 37 cm
• Use π = 22/7

Concept / Approach:From C − r = 37, substitute C = 2πr to get r(2π − 1) = 37. Evaluate 2π − 1 with π = 22/7; solve for r; then compute area A = πr^2.

Step-by-Step Solution:2π − 1 = 2*(22/7) − 1 = 44/7 − 1 = 37/7r(37/7) = 37 ⇒ r = 37 * (7/37) = 7 cmArea A = πr^2 = (22/7) * 7^2 = (22/7) * 49 = 154 sq. cm

Verification / Alternative check:Compute C = 2πr = 2*(22/7)*7 = 44 cm. Then C − r = 44 − 7 = 37 cm, matching the condition, confirming r = 7 cm is correct.

Why Other Options Are Wrong:148 and 111 sq. cm do not correspond to any integer radius under π = 22/7 that satisfies C − r = 37. 259 sq. cm is too large; it would require a radius > 8 cm, contradicting the relation.

Common Pitfalls:Forgetting to subtract r from C, or using decimal π which complicates the arithmetic here. Using π = 22/7 makes the relation 2π − 1 an exact 37/7, giving r = 7 immediately.

Final Answer:154 sq. cm