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?

Answer 1

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 = $\frac{1}{2} d$, 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:
$c = 2 \pi r\\ c = 2 \pi (\frac{1}{2} d)\\ c = \pi d$

Now solve that equation for π (aka isolate π) to get the ratio of the circumference to the diameter:
$c = \pi d \\ \pi = \frac{c}{d}$

You know that the diameter, $d = \frac{2}{3}$, 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):
$\pi = \frac{c}{d}\\ \pi = \frac{c}{\frac{2}{3}}\\ \pi = c \times \frac{3}{2} \\ \pi = \frac{3c}{2}$

Your answer is B) 3C/2 = π. 

Answer 2

Answer:

B)3C/2 = π

Step-by-step explanation:

C = πd

C = π2/3

3C/2 = π