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Areas related to circles
If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor?
If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor?
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Areas related to circles If the perimeter of a semi circular protracto...
Understanding the Semi-Circular Protractor
A semi-circular protractor is a tool used for measuring angles, shaped like a half-circle. The perimeter of a semi-circular protractor is composed of two parts: the straight edge and the curved edge.
Components of the Perimeter
- Straight Edge: This is the diameter of the semi-circle.
- Curved Edge: This is half of the circumference of a full circle.
Formula for the Perimeter
The perimeter (P) of a semi-circular protractor can be expressed as:
P = Diameter + (1/2) * Circumference
Where the circumference of a full circle is given by the formula:
Circumference = π * Diameter
Therefore, the perimeter of the semi-circular protractor can be rewritten as:
P = Diameter + (1/2) * (π * Diameter)
This simplifies to:
P = Diameter * (1 + π/2)
Given Information
- Perimeter (P): 108 cm
Finding the Diameter
To find the diameter, we rearrange the formula:
Diameter = P / (1 + π/2)
Substituting the given perimeter:
Diameter = 108 / (1 + 3.14/2)
Calculating this:
1. Calculate π/2:
- π/2 ≈ 1.57
2. Add 1:
- 1 + 1.57 = 2.57
3. Divide:
- Diameter = 108 / 2.57 ≈ 42 cm
Final Result
The diameter of the semi-circular protractor is approximately 42 cm.
A semi-circular protractor is a tool used for measuring angles, shaped like a half-circle. The perimeter of a semi-circular protractor is composed of two parts: the straight edge and the curved edge.
Components of the Perimeter
- Straight Edge: This is the diameter of the semi-circle.
- Curved Edge: This is half of the circumference of a full circle.
Formula for the Perimeter
The perimeter (P) of a semi-circular protractor can be expressed as:
P = Diameter + (1/2) * Circumference
Where the circumference of a full circle is given by the formula:
Circumference = π * Diameter
Therefore, the perimeter of the semi-circular protractor can be rewritten as:
P = Diameter + (1/2) * (π * Diameter)
This simplifies to:
P = Diameter * (1 + π/2)
Given Information
- Perimeter (P): 108 cm
Finding the Diameter
To find the diameter, we rearrange the formula:
Diameter = P / (1 + π/2)
Substituting the given perimeter:
Diameter = 108 / (1 + 3.14/2)
Calculating this:
1. Calculate π/2:
- π/2 ≈ 1.57
2. Add 1:
- 1 + 1.57 = 2.57
3. Divide:
- Diameter = 108 / 2.57 ≈ 42 cm
Final Result
The diameter of the semi-circular protractor is approximately 42 cm.
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Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor?
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Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor?.
Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Areas related to circles If the perimeter of a semi circular protractor is 108 cm, find the diameter of the protractor?.
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