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 = [tex] \frac{1}{2} d[/tex], 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:
[tex]c = 2 \pi r\\
c = 2 \pi (\frac{1}{2} d)\\
c = \pi d[/tex]
Now solve that equation for π (aka isolate π) to get the ratio of the circumference to the diameter:
[tex] c = \pi d \\
\pi = \frac{c}{d} [/tex]
You know that the diameter, [tex]d = \frac{2}{3} [/tex], 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):
[tex]\pi = \frac{c}{d}\\
\pi = \frac{c}{\frac{2}{3}}\\
\pi = c \times \frac{3}{2} \\
\pi = \frac{3c}{2}
[/tex]
Your answer is B) 3C/2 = π.
