Cups A and B are cone shaped and have heights of 35 cm and 23 cm and openings with radii of 14 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?

1 Answer
Deepak G.
Aug 13, 2016

cup A will not overflow.

=28.5 cm

Explanation:

Total volume of cup B=pir^2h/3=pi(9)^2(23/3)=621pi
Total volume of cup A=pir^2h/3=pi(14)^2(35/3)=2286.67pi
Since volume of cup B is less than volume of cup A; Contents of cup B if poured into cup A will not make cup A overflow
hence cup A will not overflow.

So we have to find H=? the height in Cup A which will have content of same volume as volume of CupB

pi(14)^2(H/3)=pi(9)^2(23)
or

H/3=(9^2/14^2)(23)=9.5
or

H=28.5 cm

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