Drop of Paint
A drop of paint fell onto a horizontal flat sheet of clean glass. We suppose that at a particular instant the drop forms a perfect sphere in the air. The paint has spread out into a uniform circular disc of a diameter that is twice as large as the initial sphere diameter.
What is the ratio of the disc thickness to the initial diameter of the drop?
(Problem is not original)
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1 solution
Volume of sphere = 4/3 pi r^3
Volume of the cylindrical disc of twice the diameter (twice the radius) of the sphere = h x pi (2r)^2 where h is the thickness of the disc
The volumes are equal
4/3 pi r^3 = 4 pi r^2 x h
r/3 = h, r = d/2
thus d/6 = h