Cups A and B are cone shaped and have heights of 39 cm and 22 cm and openings with radii of 17 cm and 13 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 14, 2016

cup A will not overflow.
Height=12.865 cm

Explanation:

Total volume of cup B=pir^2h/3=pi(13)^2(22/3)=1239.33pi
Total volume of cup A=pir^2h/3=pi(17)^2(39/3)=3757pi
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(17)^2(H/3)=1239.33pi
or

H/3=1239.33/17^2=4.288
or

H=12.865 cm

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