The height and radius of the cone of which the frustum is a part are h1 and r1 respectively. If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h2 : h1 = 1 : 2, then r2 : r1 is equal to

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KollegeApply · Accepted Answer

Since, Delta AOV "and " LO'Vare similar triangles, i.e., In Delta AOV "and " LO'V OA/O'L = OV/O'V \Rightarrow r_1/r_2 = h_1/h_1 - h_2 \Rightarrow \left( h_1 - h_2 \right) r_1 = h_1 r_2 \Rightarrow r_1 h_1 - r_1 h_2 = h_1 r_2 \Rightarrow r_1 h_1 - h_1 r_2 = r_1 h_2 \Rightarrow h_1 \left( r_1 - r_2 \right) = r_1 h_2 \Rightarrow \frac{\left( r_1 - r_2 \right)}{r_1} = h_2/h_1 \Rightarrow \frac{\left( r_1 - r_2 \right)}{r_1} = $\frac{1}{2}$ \Rightarrow 1 - r_2/r_1 = $\frac{1}{2}$ \Rightarrow r_2/r_1 = 1 - $\frac{1}{2}$ = $\frac{1}{2}$ Thus, r_2 : r_1 = 1: 2 [Solution diagram: 64011_solution_1.png]

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