## Cone ComparisonsMath brain teasers require computations to solve.If the heights of two cones are in the ratio of 1:3 and their diameters in the ratio 3:5, respectively, find the ratio of their volumes.
The hint will give you the equation for the volume of a cone if you don't know it. ## AnswerRatio of their volumes = 3:25.The volume of cone 1 is: V(1) = 1/3 * pi * r(1)^2 * h(1) Expressed in terms of r(1) and h(1), the volume of cone 2 is: V(2) = 1/3 * pi * (5/3*r(1))^2 * (3*h(1)) If you divide the first equation by the second, you get: V(1)/V(2) = 9/25 * 1/3 (all other terms cancel) V(1) / V(2) = 3/25 Hide ## What Next?
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