Cups A and B are cone shaped and have heights of 27cm and 24cm and openings with radii of 5cm and 14cm, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

1 Answer
Aug 24, 2016

A will overflow.

Explanation:

Remember that:Vcone=πr2h3

VA=π×52×273andVB=π×142×243

We do not need the actual volumes, we just need to know which one is greater. πand3 are common to bother and therefore can be ignored in the comparison.

A:52×27=675 and B:142×24=4,704

The volume of B is significantly bigger than A.
A will overflow (several times if A is emptied between fills)