Bachelor Kitchen Word Problem

Mr. Walker has an old can opener from his family’s garage. Since all of the food in Mr. Walker’s Bachelor Kitchen is in cans, he uses the opener quite a lot. You might say he’s developed a relationship with it. Anyway, as a result of the excessive use, the can opener’s “cutting disc” (the rotating metal disc that cuts into the top of the can) developed a tiny––but promiscuous––bend in one place. Since Mr. Walker is too cheap, and is obsessed with conserving resources anyway, he will not replace the can opener. Since Mr. Walker is a math teacher, he’ll instead torture his students (and blog followers) with a math problem.

Now, instead of cutting completely around the circumference of the can without a hitch, like a can opener should do, the bend in the disc causes this slacker can opener to dislodge from the edge and run itself off of the can. Tonight Mr. Walker noticed with intrigue that it runs itself off of a can exactly pi times (that is, if the disc is positioned with the bend against the can so that it starts cutting into the lid right at the bend in the disc, so that the disc rotates once fully before hitting the bend again and running off the can, it will run off three times with .14159... left over of the can’s circumference to cut.)(This is true) Mr. Walker quickly opened every can in the cupboard to make sure that his observation was correct (which it was), and as smells of butternut squash soup, green peas, and petite diced tomatoes wafted from the kitchen he measured the diameter of the can to be exactly 7.5 cm.

So now the question is this, my friends: What is the ratio of the diameter of the can to the diameter of the can opener’s cutting disc?

The first to answer correctly in the comments section wins a prize! (Maybe a can of already-opened butternut squash soup?)