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The difference between the circumference and radius of a circle is37 m. What is the circumference of the circle?
- a)7m
- b)44m
- c)154m
- d)88m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The difference between the circumference and radius of a circle is37m....
2πr − r = 37
r = 37/2π−1 = 
= 7m
= 7mCircumference = 2πr = 2 × 22/7 × 7 = 44m
Most Upvoted Answer
The difference between the circumference and radius of a circle is37m....
Understanding the Problem
The problem states that the difference between the circumference (C) and the radius (r) of a circle is 37 meters. We need to find the circumference of the circle.
Formulas Involved
To solve this, we use the formulas:
- Circumference of a circle: C = 2πr
- Given condition: C - r = 37
Setting Up the Equation
From the given condition, we can express C in terms of r:
- C = r + 37
Now, substituting the formula for circumference into this equation gives:
- 2πr = r + 37
Solving for Radius
To isolate r, we can rearrange the equation:
- 2πr - r = 37
- (2π - 1)r = 37
- r = 37 / (2π - 1)
Using the approximate value of π (3.14) helps in calculating:
- 2π ≈ 6.28
- 2π - 1 ≈ 5.28
Thus,
- r ≈ 37 / 5.28 ≈ 7 meters
Finding the Circumference
Now that we have r, we can find C:
- C = 2πr
- C ≈ 2 * 3.14 * 7 ≈ 44 meters
Conclusion
The circumference of the circle is approximately:
- C = 44 meters
Thus, the correct answer is option 'b' - 44m.
The problem states that the difference between the circumference (C) and the radius (r) of a circle is 37 meters. We need to find the circumference of the circle.
Formulas Involved
To solve this, we use the formulas:
- Circumference of a circle: C = 2πr
- Given condition: C - r = 37
Setting Up the Equation
From the given condition, we can express C in terms of r:
- C = r + 37
Now, substituting the formula for circumference into this equation gives:
- 2πr = r + 37
Solving for Radius
To isolate r, we can rearrange the equation:
- 2πr - r = 37
- (2π - 1)r = 37
- r = 37 / (2π - 1)
Using the approximate value of π (3.14) helps in calculating:
- 2π ≈ 6.28
- 2π - 1 ≈ 5.28
Thus,
- r ≈ 37 / 5.28 ≈ 7 meters
Finding the Circumference
Now that we have r, we can find C:
- C = 2πr
- C ≈ 2 * 3.14 * 7 ≈ 44 meters
Conclusion
The circumference of the circle is approximately:
- C = 44 meters
Thus, the correct answer is option 'b' - 44m.
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The difference between the circumference and radius of a circle is37m. What is the circumference of the circle?a)7mb)44mc)154md)88mCorrect answer is option 'B'. Can you explain this answer?
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