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A wire is in the form of a square with side 66 cm. If it is bent into a circle, then what is the radius of the circle?
- a)42
- b)36
- c)45
- d)33
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A wire is in the form of a square with side 66 cm. If it is bent into ...
Given:
A wire is in the shape of a square of side 66 cm
Formula Used:
The perimeter of a Square = 4 × Side
The perimeter of a Circle = 2πr
Calculation:
According to the question,
Perimeter of Square = Perimeter of Circle
⇒ 4 × 66 = 2 × (22/7) × r
⇒ 2 × 3 = r/7
⇒ r = 42 cm
∴ The radius of the circle is 42 cm.
A wire is in the shape of a square of side 66 cm
Formula Used:
The perimeter of a Square = 4 × Side
The perimeter of a Circle = 2πr
Calculation:
According to the question,
Perimeter of Square = Perimeter of Circle
⇒ 4 × 66 = 2 × (22/7) × r
⇒ 2 × 3 = r/7
⇒ r = 42 cm
∴ The radius of the circle is 42 cm.
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Community Answer
A wire is in the form of a square with side 66 cm. If it is bent into ...
To find the radius of the circle, we need to calculate the length of the wire when it is bent into a circle.
The wire is in the form of a square, so each side of the square is 66 cm. Since a square has four equal sides, the total length of the wire is 4 times the length of one side of the square.
Therefore, the total length of the wire is 4 * 66 cm = 264 cm.
To find the radius of the circle, we can use the formula for the circumference of a circle, which is given by C = 2πr, where C is the circumference and r is the radius.
We know that the circumference of the circle is equal to the length of the wire, which is 264 cm.
Therefore, we can substitute these values into the formula and solve for the radius:
264 cm = 2πr
Dividing both sides of the equation by 2π, we get:
r = 264 cm / (2π)
Simplifying the expression, we have:
r = 132 cm / π
To find the value of r, we need to divide 132 cm by the value of π.
Using an approximation of π as 3.14, we can calculate the value of r as follows:
r ≈ 132 cm / 3.14 ≈ 42 cm
Therefore, the radius of the circle is approximately 42 cm, which corresponds to option A.
The wire is in the form of a square, so each side of the square is 66 cm. Since a square has four equal sides, the total length of the wire is 4 times the length of one side of the square.
Therefore, the total length of the wire is 4 * 66 cm = 264 cm.
To find the radius of the circle, we can use the formula for the circumference of a circle, which is given by C = 2πr, where C is the circumference and r is the radius.
We know that the circumference of the circle is equal to the length of the wire, which is 264 cm.
Therefore, we can substitute these values into the formula and solve for the radius:
264 cm = 2πr
Dividing both sides of the equation by 2π, we get:
r = 264 cm / (2π)
Simplifying the expression, we have:
r = 132 cm / π
To find the value of r, we need to divide 132 cm by the value of π.
Using an approximation of π as 3.14, we can calculate the value of r as follows:
r ≈ 132 cm / 3.14 ≈ 42 cm
Therefore, the radius of the circle is approximately 42 cm, which corresponds to option A.
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