A circle's diameter is 105 cm less than its circumference. What is the circle's diameter?
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Answer: D. 49 cm
Explanation
The circumference of a circle is calculated by multiplying pi by its diameter. The difference between the circumference and the diameter is given as one hundred five centimeters. Factoring out the diameter leaves the diameter multiplied by pi minus one, yielding forty nine centimeters. The mathematical constant pi represents the ratio of a circle circumference to its diameter. Algebraic factoring simplifies equations by grouping common terms together before division. Linear geometric dimensions are expressed in standard units of length such as centimeters.
Mechanical engineers use circumference and diameter relationships to design rotating pulleys and gears. Carpenters and metalworkers apply circle formulas when cutting circular components from raw materials. Geometry problems often combine perimeter and diameter constraints to test algebraic manipulation skills. Option A is incorrect because it fails to satisfy the specified difference with the circumference. Option B underestimates the diameter required to create a difference of one hundred five centimeters. Option C results from a minor estimation error during the final algebraic division step.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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