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It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
- a)10 m
- b)15 m
- c)20 m
- d)24 m
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
It is proposed to build a single circular park equal in area to the su...
Given:
- The diameter of the first circular park is 16 m.
- The diameter of the second circular park is 12 m.
To find:
- The radius of the new park.
Solution:
We need to find the radius of the new circular park, which is equal in area to the sum of the areas of the two given circular parks.
Area of a circle:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle.
Area of the first park:
The diameter of the first park is 16 m. So, the radius (r1) of the first park is half of the diameter, which is 16/2 = 8 m.
The area (A1) of the first park is given by A1 = π(8)² = 64π square meters.
Area of the second park:
The diameter of the second park is 12 m. So, the radius (r2) of the second park is half of the diameter, which is 12/2 = 6 m.
The area (A2) of the second park is given by A2 = π(6)² = 36π square meters.
Area of the new park:
The area (A) of the new park is the sum of A1 and A2.
A = A1 + A2
A = 64π + 36π
A = 100π square meters.
Radius of the new park:
To find the radius (r) of the new park, we need to use the formula for the area of a circle.
A = πr²
100π = πr²
r² = 100
r = √100
r = 10 m.
Therefore, the radius of the new park is 10 m. Hence, the correct answer is option A.
- The diameter of the first circular park is 16 m.
- The diameter of the second circular park is 12 m.
To find:
- The radius of the new park.
Solution:
We need to find the radius of the new circular park, which is equal in area to the sum of the areas of the two given circular parks.
Area of a circle:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle.
Area of the first park:
The diameter of the first park is 16 m. So, the radius (r1) of the first park is half of the diameter, which is 16/2 = 8 m.
The area (A1) of the first park is given by A1 = π(8)² = 64π square meters.
Area of the second park:
The diameter of the second park is 12 m. So, the radius (r2) of the second park is half of the diameter, which is 12/2 = 6 m.
The area (A2) of the second park is given by A2 = π(6)² = 36π square meters.
Area of the new park:
The area (A) of the new park is the sum of A1 and A2.
A = A1 + A2
A = 64π + 36π
A = 100π square meters.
Radius of the new park:
To find the radius (r) of the new park, we need to use the formula for the area of a circle.
A = πr²
100π = πr²
r² = 100
r = √100
r = 10 m.
Therefore, the radius of the new park is 10 m. Hence, the correct answer is option A.
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Community Answer
It is proposed to build a single circular park equal in area to the su...
Πr×r+πr×r=πr×r
8.8+6.6=r.r
r=10
8.8+6.6=r.r
r=10
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It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer?.
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer?.
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It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would bea)10 mb)15 mc)20 md)24 mCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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