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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?
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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?
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