Question

Cups A and B are cone shaped and have heights of `27 cm` and `24 cm` and openings with radii of `5 cm` and `14 cm`, 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?

Answer 1

A will overflow.

Explanation:

Remember that:`V_"cone" = (pi r^2h)/3`

`V_A = (pixx 5^2xx27)/3 and V_B= (pi xx14^2xx24)/3`

We do not need the actual volumes, we just need to know which one is greater. `pi and 3` are common to bother and therefore can be ignored in the comparison.

`A: 5^2 xx27 = 675 " "and " "B: 14^2 xx24 = 4,704`

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