Question

Cups A and B are cone shaped and have heights of `22 cm` and `25 cm` and openings with radii of `6 cm` and `11 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

Cup A will overflow.

Explanation:

cone volume `=pir^2(h/3)`
where r=radius, h=height
Cup B volume = `pi11^2(25/3)=3167.8`
Cup A volume = `pi6^2(22/3)=829.4 < 3167.8`
=> Cup A will overflow

Since Cup B has a greater height and radius than Cup A does, we know that Cup B has a bigger volume than Cup A. Hope this helps.