Question

Given a circle with a diameter of 2/3, which equation expresses π as the ratio of the circumference of a circle to its diameter?

A) 2C/3 = π
B) 3C/2 = π
C) 4C/3 = π
D)3C/4 = π

Answer 1

B)3C/2 = π

Explanation:

C = πd

C = π2/3

3C/2 = π

Answer 2

The circumference of a circle can be found using the equation: c = 2πr, where c=circumference and r=radius.
The radius of the circle is also equal to half the diameter: r =
`(1)/(2) d`, where r=radius and d=diameter.

Plug the equation for the radius of the circle into the equation for the circumference of the circle and simplify to get an equation that relates circumference and diameter:

`c = 2 \pi r\\ c = 2 \pi ((1)/(2) d)\\ c = \pi d`

Now solve that equation for π (aka isolate π) to get the ratio of the circumference to the diameter:

`c = \pi d \\ \pi = (c)/(d)`

You know that the diameter,
`d = (2)/(3)`, so plug that into your ratio to get your answer. Remember that dividing by a fraction is equal to multiplying by the inverse of that fraction (aka the fraction flipped):

`\pi = (c)/(d)\\ \pi = (c)/((2)/(3))\\ \pi = c * (3)/(2) \\ \pi = (3c)/(2)`

Your answer is B) 3C/2 = π.