# CirclesWhat is the ratio of the circumferences of two circles that have diameters in the ratio 1:5 ?

pohnpei397 | Certified Educator

The ratio of the circumferences of these circles is also 1:5.

The reason for this is that the circumference of a circle can be found by the formula circumference = diameter*pi.  To find the circumference of each circle, you simply multiply its diameter by pi.  Since you are multiplying both diameters by the same number, the ratio of the products (the circumferences) will be the same as the ratio of the diameters.

For example, the circumference of a circle with a diameter of 1 unit is 3.14 units.  The circumference of a circle with a diameter of 5 units is 15.7 units.  The ratio of these circumferences is 1:5.

Therefore, the ratio of the circumferences of these circles is 1:5.

giorgiana1976 | Student

Suppose that the radius of circles are: D1 and D2.

We'll express the ratio of the 2 diameters as:

D1/D2=1/5

The diameter of a circle is twice the radius of the circle, so:

D1/D2=2*R1/ 2*R2=R1/R2=1/5

The length of the circle = the circumference of the circle = 2*pi*R.

The length of the first circle = 2*pi*R1

The length of the second circle = 2*pi*R2

The ratio of the circumferences of the 2 circles:

2*pi*R1/2*pi*R2

Simplifying constant pi and 2 , we'll get:

2*pi*R1/2*pi*R2=R1/R2

But R1/R2=1/5

2*pi*R1/2*pi*R2=R1/R2=1/5