Explanation:

- Calculate the Volume of Sphere:

- A sphere's volume is given by \((4/3) \pi r^3\).

- For a sphere of radius 6 cm, volume \(= (4/3) \pi (6)^3 = 288\pi \text{ cm}^3\).

- Volume Equivalence:

- Volume of sphere = Volume of wire

- Volume of the Wire:

- Wire is cylindrical in shape.

- Volume of cylinder = \(\pi r^2 h\), where \(r\) is the radius and \(h\) is the height (length).

- Setup Equation:

- Volume of wire = \(\pi (8)^2 h = 64\pi h\)

- Equating it with sphere's volume: \(64\pi h = 288\pi\).

- Solve for Length (h):

- Simplify: \(h = 288/64\)

- Length \(h = 4.5 \text{ cm}\).

- Correct Option:

- Option:3 - 4.5 cm