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Cups A and B are cone shaped and have heights of #28 cm# and #23 cm# and openings with radii of #6 cm# and #12 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

James Atkins

cup A will overflow.

Volume (V) of cone =# 1/3pir^2h# where h represents height and r , the radius.

#V_A = 1/3pixx6^2xx28 = 336pi ≈ 1055.575 " cubic cm " #

and #V_B = 1/3pixx12^2xx23 = 1104pi ≈ 3468.318 " cubic cm "#

since # V_B > V_A " cup A will overflow " #

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Answer 2

James Atkins

Cup A will not overflow when the contents of Cup B are poured into it. After pouring, Cup A will be filled up to a height of 28 cm, which is its original height, as Cup B has a smaller volume than Cup A.

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Answer from HIX Tutor

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