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A circular wire of radius 56 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is
- a)70cm
- b)75cm
- c)80cm
- d)85cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A circular wire of radius 56 cm is cut and bent in the form of a recta...
The perimeter of the circle, that is, the rectangle is,
P=2πr = 2 * 22/7 * 56 =16×22 cm.
Let us assume the actual length and breadth of the rectangle be, 6xand 5x
So perimeter will be,
P=2(6x+5x)=22x
16×22=22x
X=16.
The smaller side or breadth =5x=80cm
P=2πr = 2 * 22/7 * 56 =16×22 cm.
Let us assume the actual length and breadth of the rectangle be, 6xand 5x
So perimeter will be,
P=2(6x+5x)=22x
16×22=22x
X=16.
The smaller side or breadth =5x=80cm
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Community Answer
A circular wire of radius 56 cm is cut and bent in the form of a recta...
Given:
Radius of the circular wire = 56 cm
Ratio of sides of the rectangle = 6:5
We need to find the length of the smaller side of the rectangle.
Concept:
When a circular wire is cut and bent in the form of a rectangle, the perimeter of the rectangle is equal to the circumference of the circle.
Let's solve this step by step:
1. Circumference of the circle:
The circumference of a circle is given by the formula:
C = 2πr
Given that the radius of the circular wire is 56 cm, we can calculate the circumference:
C = 2π(56)
C = 112π cm
2. Perimeter of the rectangle:
The perimeter of a rectangle is given by the formula:
P = 2(l + b)
Let the length of the rectangle be 6x.
Then, the breadth of the rectangle will be 5x.
So, the perimeter of the rectangle is:
P = 2(6x + 5x)
P = 2(11x)
P = 22x
Since the perimeter of the rectangle is equal to the circumference of the circle, we can equate these two values:
22x = 112π
3. Finding the value of x:
Dividing both sides of the equation by 22, we get:
x = (112π) / 22
x = 4π
4. Finding the length of the smaller side of the rectangle:
The length of the smaller side of the rectangle is 5x.
Substituting the value of x, we get:
Length = 5(4π)
Length = 20π
Approximating the value of π to 3.14, we get:
Length ≈ 20(3.14)
Length ≈ 62.8 cm
Therefore, the length of the smaller side of the rectangle is approximately 62.8 cm.
Since none of the given options match the calculated value, the correct answer is None of these.
Radius of the circular wire = 56 cm
Ratio of sides of the rectangle = 6:5
We need to find the length of the smaller side of the rectangle.
Concept:
When a circular wire is cut and bent in the form of a rectangle, the perimeter of the rectangle is equal to the circumference of the circle.
Let's solve this step by step:
1. Circumference of the circle:
The circumference of a circle is given by the formula:
C = 2πr
Given that the radius of the circular wire is 56 cm, we can calculate the circumference:
C = 2π(56)
C = 112π cm
2. Perimeter of the rectangle:
The perimeter of a rectangle is given by the formula:
P = 2(l + b)
Let the length of the rectangle be 6x.
Then, the breadth of the rectangle will be 5x.
So, the perimeter of the rectangle is:
P = 2(6x + 5x)
P = 2(11x)
P = 22x
Since the perimeter of the rectangle is equal to the circumference of the circle, we can equate these two values:
22x = 112π
3. Finding the value of x:
Dividing both sides of the equation by 22, we get:
x = (112π) / 22
x = 4π
4. Finding the length of the smaller side of the rectangle:
The length of the smaller side of the rectangle is 5x.
Substituting the value of x, we get:
Length = 5(4π)
Length = 20π
Approximating the value of π to 3.14, we get:
Length ≈ 20(3.14)
Length ≈ 62.8 cm
Therefore, the length of the smaller side of the rectangle is approximately 62.8 cm.
Since none of the given options match the calculated value, the correct answer is None of these.
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