Explanation:

- The volume \( V \) of a sphere is given by the formula:

$$ V = \frac{4}{3} \pi r^3 $$

where \( r \) is the radius.

- For the initial radius of 7 cm,

$$ V_1 = \frac{4}{3} \pi (7)^3 $$

$$ V_1 = \frac{4}{3} \pi \times 343 $$

$$ V_1 = \frac{1372}{3} \pi $$

- For the final radius of 14 cm,

$$ V_2 = \frac{4}{3} \pi (14)^3 $$

$$ V_2 = \frac{4}{3} \pi \times 2744 $$

$$ V_2 = \frac{10976}{3} \pi $$

- The ratio of the volumes is:

$$ \frac{V_1}{V_2} = \frac{\frac{1372}{3} \pi}{\frac{10976}{3} \pi} $$

$$ \frac{V_1}{V_2} = \frac{1372}{10976} $$

$$ \frac{V_1}{V_2} = \frac{1}{8} $$

- Correct Ratio: 1 : 8

- Correct Option: Option 3 - 1 : 8