Cups A and B are cone shaped and have heights of #27 cm# and #25 cm# and openings with radii of #7 cm# and #9 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?

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Answer 1 · 2017-11-19T17:03:21

Yes, cup A will overflow.

Find the volume of each cone by using the following formula:
#V=pir^2(h/3)#

#V_A=pi49(27/3)=441picm^3#
#V_B=pi81(25/3)=675picm^3#

Since cone B has a greater volume than cone A, and it is given that cone B is completely full, it can be concluded that cup A will overflow.