a wire of radius 3mm and length 200m is melted into a sphere. Calculate the radius of the sphere in meters

To find the radius formed by melting the wire, you must start with this equation:

volume of wire = volume of sphere (since it is simply melted into a different shape, the volume would remain the same, equal)

πr²l = 4/3πr³

cancel π:

r²l = 4/3r³

3r²l = 4r³

r³ = (3r²l)/4

r³ = (3 × 3² × 200)/4

r³ = 1350

r = (cube root) of 1350

r = 11.052094

r = 11.05 mm

divide by 1000 to get the answer in the unit meters:

r = 0.01105m