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

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 = , 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:


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


You know that the diameter, , 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):


Your answer is B) 3C/2 = π. 

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