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A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle?
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A chord is substation and angle of 90 degree at the centre of a circle...
Understanding the Problem
To find the area of the minor segment corresponding to a chord that subtends a 90-degree angle at the center of a circle with a radius of 14 cm, we can break the problem down into manageable steps.
Step 1: Calculate the Area of the Sector
- The angle θ in radians for a 90-degree angle is:
θ = 90 × (π / 180) = π/2
- The formula for the area of a sector is given by:
Area of Sector = (θ/2) × r²
Substituting the values:
Area of Sector = (π/2) × (14)²
= (π/2) × 196
= 98π cm²
Step 2: Calculate the Area of the Triangle
- The triangle formed by the radius and the chord is an isosceles right triangle since it subtends a 90-degree angle.
- The area of the triangle can be calculated using:
Area of Triangle = (1/2) × base × height
Here, both base and height are equal to the radius (14 cm):
Area of Triangle = (1/2) × 14 × 14
= 98 cm²
Step 3: Calculate the Area of the Minor Segment
- The area of the minor segment can be found by subtracting the area of the triangle from the area of the sector:
Area of Minor Segment = Area of Sector - Area of Triangle
= 98π - 98 cm²
Final Calculation
- The area of the corresponding minor segment of the circle is:
Area = 98(π - 1) cm²
Thus, the area of the minor segment corresponding to the chord is approximately 98(3.14 - 1) cm², which can be further calculated if needed.
To find the area of the minor segment corresponding to a chord that subtends a 90-degree angle at the center of a circle with a radius of 14 cm, we can break the problem down into manageable steps.
Step 1: Calculate the Area of the Sector
- The angle θ in radians for a 90-degree angle is:
θ = 90 × (π / 180) = π/2
- The formula for the area of a sector is given by:
Area of Sector = (θ/2) × r²
Substituting the values:
Area of Sector = (π/2) × (14)²
= (π/2) × 196
= 98π cm²
Step 2: Calculate the Area of the Triangle
- The triangle formed by the radius and the chord is an isosceles right triangle since it subtends a 90-degree angle.
- The area of the triangle can be calculated using:
Area of Triangle = (1/2) × base × height
Here, both base and height are equal to the radius (14 cm):
Area of Triangle = (1/2) × 14 × 14
= 98 cm²
Step 3: Calculate the Area of the Minor Segment
- The area of the minor segment can be found by subtracting the area of the triangle from the area of the sector:
Area of Minor Segment = Area of Sector - Area of Triangle
= 98π - 98 cm²
Final Calculation
- The area of the corresponding minor segment of the circle is:
Area = 98(π - 1) cm²
Thus, the area of the minor segment corresponding to the chord is approximately 98(3.14 - 1) cm², which can be further calculated if needed.
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A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle?
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A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle?.
A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A chord is substation and angle of 90 degree at the centre of a circle of radius 14 cm find the area of the corresponding minor segment of the circle?.
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