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.
HintThe volume of a cone is:
V = 1/3 * pi * r^2 * h
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
See another brain teaser just like this one...
Or, just get a random brain teaser
If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.
Back to Top