Explanation:

To solve this problem, we need to equate the volume of the sphere to the volume of the cylinder since the sphere is melted and recast into the cylinder. Here's the process:

- Volume of Sphere:

- Formula: \(\frac{4}{3} \pi r^3\)

- Sphere radius: 8.4 cm

- Volume: \(\frac{4}{3} \times \pi \times (8.4)^3\)

- Volume of Cylinder:

- Formula: \(\pi R^2 h\)

- Cylinder radius: 12 cm

- Volume: \(\pi \times (12)^2 \times h\)

- Setting the sphere's volume equal to the cylinder’s volume to find height \(h\):

- \(\frac{4}{3} \times \pi \times 8.4^3 = \pi \times 12^2 \times h\)

- Solve for \(h\):

- \(h = \frac{4 \times 8.4^3}{3 \times 12^2}\)

- Calculate \(h\) to find it equals approximately 5.5 cm

- Therefore, the height of the cylinder is around 5.5 cm.

Correct Answer: Option 4: 5.5 cm