Two solid right circular cones have the same height. The radii of their bases are r1 and r2. They are melted and recast into a cylinder of same height. Show that the radius of the base of the cylinder is √r21+r223.
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Solution
Let h be the height of the two given cones of base radii r1 and r2 respectively.
Let R be the radius of the cylinder.
Height of cylinder and cones = h (given)
by given data,
Volume of the cylinder = Sum of the volumes of two cones