Circle O has a circumference of approximately [tex]$250 \pi ft$[/tex]. What is the approximate length of the diameter?
A. 40 ft
B. 80 ft
C. 125 ft
D. 250 ft
Answer (2)
Recall the formula for the circumference of a circle: C = π d .
Substitute the given circumference C = 250 π ft into the formula: 250 π = π d .
Divide both sides of the equation by π to solve for the diameter: d = π 250 π = 250 .
Conclude that the diameter of the circle is approximately 250 ft.
Explanation
Problem Analysis We are given a circle O with a circumference of approximately 250 π ft. Our goal is to find the approximate length of the diameter of this circle.
Recall the Circumference Formula The formula for the circumference of a circle is given by: C = π d where:
C is the circumference of the circle,
d is the diameter of the circle.
Substitute the Given Circumference We are given that the circumference C = 250 π ft. We can substitute this value into the formula: 250 π = π d
Solve for the Diameter To find the diameter d , we need to isolate d by dividing both sides of the equation by π :
π 250 π = π π d d = 250 So, the diameter of the circle is approximately 250 ft.
Final Answer The approximate length of the diameter of circle O is 250 ft.
Examples
Understanding the relationship between a circle's circumference and diameter is useful in many real-world scenarios. For example, if you're designing a circular garden and know you want the fence around it (the circumference) to be approximately 250 π feet long, you can quickly calculate that the diameter of the garden should be about 250 feet. This helps in planning the layout and ensuring you have enough space for your plants!
The diameter of circle O is approximately 250 ft, which we calculated using the formula for circumference. To find this, we substituted the given circumference into the formula and solved for diameter. Therefore, the correct answer is option D: 250 ft.
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