30 metallic cylinders of same size are melted and cast in the form of cones having the same radius a...........

Quantitative Aptitude (CDS) Mensuration 3D

30 metallic cylinders of same size are melted and cast in the form of cones having the same radius and height as those of the cylinders.

Consider the following statements:

Statement I : A maximum of 90 cones will be obtained.

Statement II : The curved surface of the cylinder can be flattened in the shape of a rectangle but the curved surface of the cone when flattened has the shape of triangle

Which one of the following is correct in respect of the above?

Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I

Both Statement I and Statement II are correct and Statement II is not the correct explanation of Statement I

Statement I is correct but Statement II is not correct

Statement I is not correct but Statement II is correct

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Explanation:

Let the radius and height of the cone and cylinder be r and h, respectively.
Suppose the number of cones obtained be n.
Therefore, 30 × Volume of each cylinder = n × Volume of each cone

Hence, statement I is correct.

The curved surface of the cylinder can be flattened in the shape of a rectangle but the curved surface of the cone when flattened has the shape of a sector.
Hence, statement II is not correct.