Question

A 80 cm rope is bend in th circular form . find its radius​

Answer 1

Answer:

The radius of the rope would be 12.73 cm

Step-by-step explanation:

circumference of the circle = 2πr = 80 cm

2 * 22/7 * r = 80

r = (80*7)/(2*22)

r = 12.7272... = 12.73 cm = radius.

Answer 2

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A 80 cm rope is bend in th circular form . find its radius

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Radius of the circle obtained: ≈42cm≈42cm.

Side of the square formed: 66cm66cm.

Solution:

Since the wire is bent in the form of a circle, length of wire is now the circumference of the circle.

If r is the radius of the circle, we can establish the relationship between circumference of circle and length of wire as: 2πr=2642πr=264

Using the approximation of π=227π=227, we can compute radius to be:

r=264∗72∗22=42r=264∗72∗22=42

If the wire is bent in the shape of a square, perimeter of the square is equal to the length of the wire.

If a is the length of the side of the square, we can establish the relationship between perimeter of square and length of wire as:

4a=2644a=264

So,

a=264/4=66a=264/4=66

Additional insights:

The circle’s diameter is larger than the square’s side i.e. the square is inscribed within the circle.

In fact, it can be proven that given a fixed perimeter, a circle is the shape with maximum area.

Proof:

Relationship between area of a regular n-gon using perimeter and apothem is:

A=pa2A=pa2

Relationship between area of a circle using perimeter and radius is:

Area of a circle: pr2pr2

a is the inradius of the regular n-gon and hence is always smaller than the circumradius r

Hope it helps u

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