Question

The circumference of a circle with the diameter of 3 cm is 9.42 cm. What is the ratio of the circumference to the diameter?

Answer 1

I think you divide circumference by diameter, I haven't done this in the longest so I am rusty in this

\(\large{\frac{9.42}{3}}\)

Answer 2

ok

Answer 3

How would you use a model to determine the approximate formula for the area of a circle with a diameter of 8 cm, and connect the model to the actual formula?

Answer 4

What about that one?

Answer 5

yikes! the ratio of the circumference of the circle to the diameter is always \(\pi\)
that is a good definition of \(\pi\)
one wonders what kind of math teacher writes questions like these?

Answer 6

so if we hypothesise that the ratio of the circumference (C) of the circle to the diameter (D) is actually always some constant \(\xi\):

ie \(\dfrac{C}{ D} = \xi\),

....then we set about finding the value of \(\xi\)

So how do we do that?

This is actually, IMHO, a good teaching strategy.

If you think it's obvious that \(\xi = \text{whatever}\), then go and prove it !!

And then prove that it is \(\xi\) is constant