Diameter 105 cm less than circumference: For a circle, the diameter is 105 cm less than its circumference. Find the diameter.

Introduction / Context:This linear relation between circumference and diameter can be solved algebraically using C = πd. Rearranging yields the diameter directly.

Given Data / Assumptions:

• d = diameter
• C = circumference = πd
• d = C − 105

Concept / Approach:Substitute C = πd into d = C − 105 to get d = πd − 105 → (π − 1)d = 105 → d = 105 / (π − 1). Use π = 22/7 for an exact result.

Step-by-Step Solution:π − 1 = 22/7 − 1 = 15/7d = 105 / (15/7) = 105 * 7 / 15 = 49 cm

Verification / Alternative check:C ≈ π * 49 ≈ 153.94 cm; C − d ≈ 104.94 cm, which equals 105 cm with π = 22/7 exactly.

Why Other Options Are Wrong:44–52 cm values do not satisfy d = πd − 105 when substituted back.

Common Pitfalls:Using radius instead of diameter; subtracting 105 from π instead of from the circumference; numerical rounding too early.

Final Answer:49 cm