A solid cylinder with a conical cavity as shown in the figure is melted and cast into 4 identical solid spheres. What is the ratio of the radius of one sphere and that of the given solid?

Answers
Given : A solid cylinder with a conical cavity is melted and cast
into 4 identical solid spheres
To Find : ratio of the radius of one sphere and that of the given solid
Solution:
Radius of cylinder = r
Volume of cylinder = πr²h
Volume of conical cavity = (1/3)πr²h
Hence Volume = πr²h - (1/3)πr²h = (2/3)πr²h
melted and cast into 4 identical solid spheres
Radius of Sphere = R
Volume of one sphere = (4/3) πR³
=> Volume of 4 spheres = 4 * (4/3) πR³ = (16/3) πR³
(16/3) πR³ = (2/3)πr²h
=> 8R³ = r²h
Height of cylinder also needed to find ratio of radius of sphere to radius of cylinder.
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