Explanation:

- Volume of the sphere: The formula is \( \frac{4}{3} \pi r^3 \). For the sphere with radius 15 cm, this becomes \( \frac{4}{3} \pi (15)^3 \) cubic cm.

- Volume of the wire: It has a cylindrical shape. The formula is \( \pi r^2 h \), where \( r \) is 1.5 cm (since 15 mm = 1.5 cm).

- Length of wire: Since the volumes remain constant when the sphere is melted into the wire, set the volume of the sphere equal to the volume of the wire, and solve for \( h \), the length of the wire.

Calculating, we find:

- Sphere's volume = \( 4/3 \, \pi \, (15)^3 = 4500 \pi \, \text{cm}^3 \)

- Wire's volume = \( \pi \, (1.5)^2 \, h = 2.25\pi h \)

Equating and solving:

- \( 4500 \pi = 2.25\pi h \)

- \( 4500 = 2.25h \)

- \( h = 2000 \, \text{cm} \)

- Correct option is: Option 4: 2000 cm

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