Explanation:

- The original sphere has a radius of 6.3 cm.

- Volume of sphere: \(V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (6.3)^3\).

- The sphere is melted to form a cone.

- Volume of cone: \(V = \frac{1}{3} \pi r^2 h\), where \(h = 25.2\) cm is given.

- Equate volumes to find the cone's base radius.

- Calculate: \(\frac{4}{3} \pi (6.3)^3 = \frac{1}{3} \pi r^2 (25.2)\).

- Calculate the base radius \(r\) and then the diameter \(2r\).

- Ratio of diameter to height:

$$

\left(\frac{2r}{25.2}\right)

$$

- After solving, you find the ratio \(\frac{1}{2}\).

Correct Answer: Option: 3 (1 : 2)