Cups A and B are cone shaped and have heights of #33 cm# and #29 cm# and openings with radii of #10 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?

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Answer 1 · 2018-07-03T03:47:55

Yes, cup A will overflow.

Given: cup A is a cone with #r = 10 cm; h = 33 cm#
#" "#cup B is a cone with #r = 13 cm; h = 29 cm#

Volume of a circular right cone: #V = 1/3 pi r^2 h#

#V_b = 1/3 pi 13^2 * 29 = 4901/3 pi ~~ 5132 " "cm^3#

#V_a = 1/3 pi 10^2 * 33 = 1100 pi ~~ 3456 " "cm^3#