Explanation:

- To find the ratio of the surface area of the original balloon to the inflated balloon, use the formula for the surface area of a sphere: \(A = 4\pi r^2\).

- Original balloon radius: 6 cm. Surface area = \(4\pi (6^2) = 144\pi\).

- Inflated balloon radius: 10 cm. Surface area = \(4\pi (10^2) = 400\pi\).

- Ratio of surface areas = \(\frac{144\pi}{400\pi} = \frac{144}{400} = \frac{9}{25}\).

- Option 4: 9:25 represents this ratio. Correct Answer

- Option 1: 4:5 doesn't match.

- Option 2: 27:125 doesn't work here.

- Option 3: 3:5 is incorrect.