A solid metal cylinder of base radius $3\,cm$ and height $5\,cm$ is melted to make $n$ solid cones fo height $1\,cm$ and base radius $1\,mm$. Then value of $n$ is

The volume of the cylinder is pi times three squared times five, which equals 45 pi cubic centimeters, and converting one millimeter to 0.1 centimeters gives the volume of one cone as one third times pi times 0.1 squared times one, equaling 0.00333 pi cubic centimeters. Dividing the cylinder's volume by the cone's volume yields 45 pi divided by 0.00333 pi, which results in 13500.

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