Question

The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?

Answer 1

`(C)/(20)=\pi`

Explanation:

It is given that radius of a circle is 10.

We need to write an equation which expresses the ratio of the circumference of the circle to the circle's diameter using π.

The circumference of the circle is

`C=2\pi r`

where, r is the radius of the circle.

Substitute r=10 in the above formula.

`C=2\pi (10)`

`C=20\pi`

Divide both sides by 20.

`(C)/(20)=(20\pi)/(20)`

`(C)/(20)=\pi`

Therefore, required equation is
`(C)/(20)=\pi`.

Answer 2

The ratio of circumference to diameter is independent of the radius.

Defining C=circumference, r=radius, D=diameter = 2r

Circumference = C = 2 π r = π D

=>

ratio of circumference / diameter

= C/D = π