Ratio of radius of the circle to perimeter of the square

To solve this question, we need to find the radius of the circle and the perimeter of the square, and then find the ratio of the two.

Finding the radius of the circle

The wire is cut into two pieces, one of which is bent into a circle. The length of the wire is 10 m. Let's assume that the length of the wire used to make the circle is x. Then, the length of the wire used to make the square is (10 - x).

The circumference of the circle is given by the formula:

C = 2πr

where C is the circumference and r is the radius of the circle.

We know that the length of the wire used to make the circle is x. Therefore:

2πr = x

r = x/(2π)

Finding the perimeter of the square

The remaining wire is used to make a square. The perimeter of the square is given by the formula:

P = 4s

where P is the perimeter and s is the length of one side of the square.

We know that the length of the wire used to make the square is (10 - x). Therefore:

4s = 10 - x

s = (10 - x)/4

Ratio of the radius of the circle to the perimeter of the square

Now that we have found the radius of the circle and the perimeter of the square in terms of x, we can find the ratio of the two:

r/P = (x/(2π))/[(10 - x)/4]

Simplifying this expression, we get:

r/P = 2x/(π(10 - x))

We need to find the ratio of the radius to the perimeter. Therefore, we can simplify the expression further:

r/P = (2x/(π(10 - x))) / 4(10 - x)/4

r/P = 2x/(π(10 - x)) * 1/4(10 - x)

r/P = 1/(2π)

Therefore, the ratio of the radius of the circle to the perimeter of the square is 1:8.

Hence, the correct answer is option B, 1:8.