### Brain Teasers

# Cone Comparisons

Math
Math 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.

The hint will give you the equation for the volume of a cone if you don't know it.

### Hint

The volume of a cone is:V = 1/3 * pi * r^2 * h

### Answer

Ratio 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

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## Comments

SInce the volume of a cone is proportional to its height and the square of its diameter then the ratio is (1/3)*(3/5)^2 = 3/25.

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