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A wire bent in the form of a circle of radius 42 cm is again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?
- a)11:12
- b)21:33
- c)22:33
- d)14:11
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A wire bent in the form of a circle of radius42cmis again bent in the ...
Length of wire = 2π × 42 = 84πcm
Let x be the side of the square. We have, 4x = 84π ⇒ x = 21π
Area of the circle: Area of the square
= π(42)2:(21π)2
= 4:π = 4:22/7 = 14:11
Let x be the side of the square. We have, 4x = 84π ⇒ x = 21π
Area of the circle: Area of the square
= π(42)2:(21π)2
= 4:π = 4:22/7 = 14:11
Most Upvoted Answer
A wire bent in the form of a circle of radius42cmis again bent in the ...
Given:
Radius of the circle = 42 cm
To find:
The ratio of the regions enclosed by the circle and the square.
Solution:
1. Area of the circle:
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius is 42 cm, we can calculate the area of the circle as follows:
A = π(42)^2 = 1764π cm^2
2. Perimeter of the square:
The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side.
Since the wire is bent in the form of a circle first and then a square, the length of the wire will be the perimeter of the square.
The circumference of the circle is equal to the length of the wire, which can be calculated as follows:
C = 2πr = 2π(42) = 84π cm
Since the wire is bent in the form of a square, the perimeter of the square will be equal to the length of the wire:
P = 84π cm
3. Length of one side of the square:
The length of one side of the square can be calculated by dividing the perimeter by 4:
s = P/4 = 84π/4 = 21π cm
4. Area of the square:
The formula to calculate the area of a square is A = s^2, where A is the area and s is the length of one side.
Given that the length of one side is 21π cm, we can calculate the area of the square as follows:
A = (21π)^2 = 441π^2 cm^2
5. Ratio of the areas:
The ratio of the areas enclosed by the circle and the square can be calculated by dividing the area of the circle by the area of the square:
Ratio = (1764π)/(441π^2) = 4/π
Simplifying this ratio, we get:
Ratio = (4/π) × (π/π) = 4/1 = 4:1
Therefore, the ratio of the regions enclosed by the circle and the square is 4:1, which is equivalent to option D, 14:11.
Radius of the circle = 42 cm
To find:
The ratio of the regions enclosed by the circle and the square.
Solution:
1. Area of the circle:
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius is 42 cm, we can calculate the area of the circle as follows:
A = π(42)^2 = 1764π cm^2
2. Perimeter of the square:
The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of one side.
Since the wire is bent in the form of a circle first and then a square, the length of the wire will be the perimeter of the square.
The circumference of the circle is equal to the length of the wire, which can be calculated as follows:
C = 2πr = 2π(42) = 84π cm
Since the wire is bent in the form of a square, the perimeter of the square will be equal to the length of the wire:
P = 84π cm
3. Length of one side of the square:
The length of one side of the square can be calculated by dividing the perimeter by 4:
s = P/4 = 84π/4 = 21π cm
4. Area of the square:
The formula to calculate the area of a square is A = s^2, where A is the area and s is the length of one side.
Given that the length of one side is 21π cm, we can calculate the area of the square as follows:
A = (21π)^2 = 441π^2 cm^2
5. Ratio of the areas:
The ratio of the areas enclosed by the circle and the square can be calculated by dividing the area of the circle by the area of the square:
Ratio = (1764π)/(441π^2) = 4/π
Simplifying this ratio, we get:
Ratio = (4/π) × (π/π) = 4/1 = 4:1
Therefore, the ratio of the regions enclosed by the circle and the square is 4:1, which is equivalent to option D, 14:11.
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A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer?
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A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer?.
A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire bent in the form of a circle of radius42cmis again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?a)11:12b)21:33c)22:33d)14:11Correct answer is option 'D'. Can you explain this answer?.
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