From here to there to there and back here!

Geometry Level pending

A metal cylinder has a volume of \(1056\text{ cm}^3\). It is melted and recast into a cone of twice the height and half the radius as the cylinder.

Now, a plane parallel to the base divides the cone in 2 parts of equal volume (1 frustum and 1 small cone). Given that both the radius and height of the small cone so formed are positive integers greater than 1.

Find the curved surface area of the original cylinder in \(\text{cm}^2\) to the nearest integer.

Details and Assumptions:

  • Use \(\pi = \frac {22}{7}\) and \( 2^{\frac{1}{3}} = 1.26.\)

  • Assume that the extra liquid metal is stored for later use.

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