It is given that the diameter of largest circle is 8 and diameter of circle is 4.
The radius of largest circle is 4.
The area of the largest circle is given by
![A_1=\pir^2](https://img.qammunity.org/2023/formulas/mathematics/college/rdj21jxsi5m0w9pgjqeb51z7g1nzblrpvu.png)
where r = 4.
Hence the area is
![16\pi](https://img.qammunity.org/2023/formulas/mathematics/college/156zv6y02e8o22z1j4mhd5iszvtdzhrih2.png)
The area of the samllest circle is given by
![a=\pi(2)^2](https://img.qammunity.org/2023/formulas/mathematics/college/2dthk1lbjrm5yw8fexdhvkrav17xh1fbui.png)
Hence the area of smallest circle is
![8\pi](https://img.qammunity.org/2023/formulas/mathematics/high-school/yk542kbwgubajnbjrdenl7cpeasbpp8p19.png)
The ratio of largest to smallest circle is given by
![\text{ratio}=(16\pi)/(8\pi)=2\colon1](https://img.qammunity.org/2023/formulas/mathematics/college/91aa4iflp8udb28ww3kazqmbwja1h3xcmm.png)
Hence the ratio is 2:1