Find the circumferences of the two circles circle a has a radius of 21 meters and circle b has a radius of 28 meters Is the relationship between the radius of a circle and the distance around the circle the same for all circles

The circumference for circle a is m.

The circumference for circle b is m.

The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as or, in a less familiar form, . The number is constant for all circles and has infinite digits, .

Step-by-step explanation:

The circumference of a circle is given by:

[1]

Where

is the circle's circumference.

is the radius of the circle.

And

is a constant value (explained below)

We can say that the distance around the circle is the circle's circumference.

The circumferences of the two circles given are:

Circle a, with radius equals to 21 meters ().

Using [1], using four decimals for , we have:

m

m

Then, the circumference for circle a is m.

Circle b, with radius equals to 28 meters ().

m

m

And, the circumference for circle b is m.

We know that

That is, the diameter of the circle is twice its radius.

Then, if we take the distance around the circle and we divided it by

This ratio, that is, the relationship between the distance around the circle (circumference) and the diameter of a circle is and is constant for all circles. This result is called the number, which is, approximately, (it has infinite number of digits).

We can observe that the relationship between the radius of a circle and the circumference is also constant:

However, this relationship is .

We can rewrite it as  

And it is also constant.