Cups A and B are cone shaped and have heights of $32 cm$ and $37 cm$ and openings with radii of $12 cm$ and $19 cm$ , 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 · 2018-06-04T13:13:27

Cup A will overflow

Volume of a cone is given by $v = 1/3pir^2h$
where h is the height and r is the radius of the cone

Volume of Cup A: $1/3pir^2h = 1/3pitimes12^2times32 = 1536pi$

Volume of Cup B: $1/3pir^2h = 1/3pitimes19^2times37=4452 1/3pi$

If Cup B is full, which has a volume of $4452 1/3pi$ which is larger than the volume of Cup A which is $1536pi$ . Therefore, Cup A will overflow.

Cups A and B are cone shaped and have heights of 32 cm32 cm and 37 cm37 cm and openings with radii of 12 cm12 cm and 19 cm19 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?