Question

Two solid right circular cones have the same height . The radii of their bases are r(1) and r(2) .They are melted and recast into a cylinder of same height show that the radius of the base of the cylinder is root r(1)square +r(2) square / 3

Answer 1

Let the radius of the base of the cylinder be R.
Volume of cylinder = volume of the two cones

pi R2h = pi r12h /3 + pi r22h/3
pi R2 h = pi h /3 (r12 + r22)
R2 = 1/3 (r12 + r22)
R = root 1/3 (r12 + r22)
Hence proved.
Hope this will help you.

Answer 2

Answer:

under root of r1 square +r2 square/3

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