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5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.?
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5. If the area of a circle is equal to sum of the areas of two cir...
Understanding the Problem
To find the diameter of the larger circle, we start with the given information about the areas of the circles. We know the diameters of two smaller circles and need to calculate the area of a larger circle that is equal to the sum of their areas.
Step 1: Calculate the Radii
- The diameter of the first circle is 10 cm, hence the radius is:
- Radius 1 = 10 cm / 2 = 5 cm
- The diameter of the second circle is 24 cm, hence the radius is:
- Radius 2 = 24 cm / 2 = 12 cm
Step 2: Calculate the Areas of the Smaller Circles
- The area of a circle is calculated using the formula:
- Area = π * r²
- For the first circle:
- Area 1 = π * (5 cm)² = 25π cm²
- For the second circle:
- Area 2 = π * (12 cm)² = 144π cm²
Step 3: Sum of Areas
- Total Area = Area 1 + Area 2
- Total Area = 25π + 144π = 169π cm²
Step 4: Set Up the Equation for the Larger Circle
- Let the radius of the larger circle be R cm. The area of the larger circle will be:
- Area = π * R²
- Setting this equal to the sum of the areas of the smaller circles:
- π * R² = 169π
Step 5: Solve for Radius and Diameter
- Cancel π from both sides:
- R² = 169
- R = √169 = 13 cm
- Therefore, the diameter of the larger circle is:
- Diameter = 2 * R = 2 * 13 cm = 26 cm
Conclusion
The diameter of the larger circle is 26 cm.
To find the diameter of the larger circle, we start with the given information about the areas of the circles. We know the diameters of two smaller circles and need to calculate the area of a larger circle that is equal to the sum of their areas.
Step 1: Calculate the Radii
- The diameter of the first circle is 10 cm, hence the radius is:
- Radius 1 = 10 cm / 2 = 5 cm
- The diameter of the second circle is 24 cm, hence the radius is:
- Radius 2 = 24 cm / 2 = 12 cm
Step 2: Calculate the Areas of the Smaller Circles
- The area of a circle is calculated using the formula:
- Area = π * r²
- For the first circle:
- Area 1 = π * (5 cm)² = 25π cm²
- For the second circle:
- Area 2 = π * (12 cm)² = 144π cm²
Step 3: Sum of Areas
- Total Area = Area 1 + Area 2
- Total Area = 25π + 144π = 169π cm²
Step 4: Set Up the Equation for the Larger Circle
- Let the radius of the larger circle be R cm. The area of the larger circle will be:
- Area = π * R²
- Setting this equal to the sum of the areas of the smaller circles:
- π * R² = 169π
Step 5: Solve for Radius and Diameter
- Cancel π from both sides:
- R² = 169
- R = √169 = 13 cm
- Therefore, the diameter of the larger circle is:
- Diameter = 2 * R = 2 * 13 cm = 26 cm
Conclusion
The diameter of the larger circle is 26 cm.
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5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.?
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5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.?.
5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5. If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.?.
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