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The difference between circumference and diameter of a circle is 105m find its radius?
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The difference between circumference and diameter of a circle is 105m ...
Understanding the Relationship Between Circumference and Diameter
The circumference (C) of a circle is directly related to its diameter (D) through the formula:
C = πD
The difference between the circumference and diameter is given as 105m:
C - D = 105m
By substituting the formula for circumference into the equation, we can find the diameter.
Step 1: Substitute the Circumference Formula
- Replace C in the equation with πD:
πD - D = 105m
Step 2: Factor Out D
- Factor D from the left side:
D(π - 1) = 105m
Step 3: Solve for Diameter (D)
- Now, we can isolate D:
D = 105m / (π - 1)
Step 4: Calculate Diameter
- Using the approximate value of π (3.14):
D ≈ 105m / (3.14 - 1)
D ≈ 105m / 2.14
D ≈ 49.06m
Step 5: Find Radius (R)
- The radius (R) is half of the diameter:
R = D / 2
R ≈ 49.06m / 2
R ≈ 24.53m
Conclusion
- The radius of the circle is approximately 24.53m. This detailed approach allows us to understand how the relationship between circumference and diameter leads to finding the radius effectively.
The circumference (C) of a circle is directly related to its diameter (D) through the formula:
C = πD
The difference between the circumference and diameter is given as 105m:
C - D = 105m
By substituting the formula for circumference into the equation, we can find the diameter.
Step 1: Substitute the Circumference Formula
- Replace C in the equation with πD:
πD - D = 105m
Step 2: Factor Out D
- Factor D from the left side:
D(π - 1) = 105m
Step 3: Solve for Diameter (D)
- Now, we can isolate D:
D = 105m / (π - 1)
Step 4: Calculate Diameter
- Using the approximate value of π (3.14):
D ≈ 105m / (3.14 - 1)
D ≈ 105m / 2.14
D ≈ 49.06m
Step 5: Find Radius (R)
- The radius (R) is half of the diameter:
R = D / 2
R ≈ 49.06m / 2
R ≈ 24.53m
Conclusion
- The radius of the circle is approximately 24.53m. This detailed approach allows us to understand how the relationship between circumference and diameter leads to finding the radius effectively.
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The difference between circumference and diameter of a circle is 105m find its radius?
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The difference between circumference and diameter of a circle is 105m find its radius? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between circumference and diameter of a circle is 105m find its radius? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between circumference and diameter of a circle is 105m find its radius?.
The difference between circumference and diameter of a circle is 105m find its radius? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between circumference and diameter of a circle is 105m find its radius? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between circumference and diameter of a circle is 105m find its radius?.
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