Question

consider two solid cones made from a uniform material. The smaller cone is a ½ scale model of the bigger one. They are released from equal height, quickly reach their terminal velocities and fall in air until they hit the ground. Use scaling reasoning to predict which cone will reach the ground first.

Answer 1

since mass varies as the scale cubed (volume),
and area varies as the scale squared,

the larger cone has a higher weight:area ratio, so it should have a higher terminal velocity.

I'm assuming the air resistance varies directly with the area. If that is not so, my logic may be wrong.