15 inch circumference to diameter
Understand the Problem
The question is asking how to convert a circumference measurement of 15 inches into its corresponding diameter. We will use the formula that connects circumference and diameter, which is C = πd, where C is circumference and d is diameter.
Answer
$4.78$ inches.
Answer for screen readers
The diameter corresponding to a circumference of 15 inches is approximately $4.78$ inches.
Steps to Solve
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Identify the formula for circumference We know that the relationship between circumference (C) and diameter (d) is given by the formula: $$ C = \pi d $$
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Rearrange the formula to solve for diameter To find the diameter, we can rearrange the formula to isolate (d): $$ d = \frac{C}{\pi} $$
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Plug in the given value for circumference Substituting the given circumference value (15 inches) into the rearranged formula: $$ d = \frac{15}{\pi} $$
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Calculate the diameter using an approximate value for π Using an approximate value of ( \pi \approx 3.14 ), we calculate: $$ d \approx \frac{15}{3.14} $$
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Finalize the calculation Perform the division: $$ d \approx 4.78 $$ inches.
The diameter corresponding to a circumference of 15 inches is approximately $4.78$ inches.
More Information
The formula ( C = \pi d ) is crucial in understanding the relationship between the circumference of a circle and its diameter. π (pi) is an irrational number approximately equal to 3.14, which is commonly used in various mathematical applications involving circles.
Tips
- Forgetting to isolate (d) correctly when rearranging the formula.
- Using an inaccurate value for ( \pi ); ensure you use a consistent level of precision.
