Explanation:

- To find the area of a circle, use the formula:

$$\text{Area}=\pi \times {\text{radius}}^2$$

- Circle-A:

- Radius: 4 cm

- Area: $\pi \times 4^2=16\pi$

- Circle-B:

- Radius: 8 cm

- Area: $\pi \times 8^2=64\pi$

- Ratio of areas (Circle-A to Circle-B):

$\frac{16\pi }{64\pi }=\frac{1}{4}$

- Option Explanation:

- Option 1: 1 : 2 (This ratio is incorrect)

- Option 2: 1 : 16 (This ratio is incorrect)

- Option 3: 1 : 8 (This ratio is incorrect)

- Option 4: 1 : 4 (This ratio is correct)

Correct Answer: Option 4 - 1 : 4