Answer:
Circumference of the circle:
![12\pi](https://img.qammunity.org/2020/formulas/mathematics/high-school/b2uvv10x6cvqiz53wfa3ukmnuk5nhfo7sg.png)
Ratio of the circumference to the diameter:
![\pi](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hvs09vob5j95u9hspf0ge6sceeo00vgyv4.png)
Explanation:
First, we are finding the circumference of the circle using the circumference formula:
![C=\pi d](https://img.qammunity.org/2020/formulas/mathematics/high-school/uhgyknhfl0dy3v41tb3ie4lm1sabrc7kui.png)
were
is the circumference of the circle
is the diameter of the circle
We know from the problem that the diameter of our circle is 12cm, so
.
Replacing values:
![C=\pi d](https://img.qammunity.org/2020/formulas/mathematics/high-school/uhgyknhfl0dy3v41tb3ie4lm1sabrc7kui.png)
![C=\pi (12)](https://img.qammunity.org/2020/formulas/mathematics/high-school/7kltq9l8jr0cus87x0vawp097hbnv4dw67.png)
![C=12\pi](https://img.qammunity.org/2020/formulas/mathematics/high-school/elh1k275ijltj52fe84v4t4fmzv570t6n4.png)
Now, to find the ratio of the circumference to the diameter, we just need to divide the circumference of our circle by the diameter:
ratio =
![(12\pi )/(12) =(\pi )/(1) =\pi](https://img.qammunity.org/2020/formulas/mathematics/high-school/81swgd41p1qud4kswr8r9r8kyozg1xg78c.png)