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Turkey NMO 2010 1st Round - P21 (Geometry)

Source:

July 26, 2012
geometry3D geometryratio

Problem Statement

A right circular cone and a right cylinder with same height 2020 does not have same circular base but the circles are coplanar and their centers are same. If the cone and the cylinder are at the same side of the plane and their base radii are 2020 and 1010, respectively, what is the ratio of the volume of the part of the cone inside the cylinder over the volume of the part of the cone outside the cylinder?
<spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 53<spanclass=latexbold>(D)</span> 43<spanclass=latexbold>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ \frac{5}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac{4}{3} \qquad<span class='latex-bold'>(E)</span>\ 1