Cups A and B are cone shaped and have heights of #32 cm# and #12 cm# and openings with radii of #15 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?

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Answer 1 · 2018-07-31T08:59:06

Cup A will be filled to a height of #7.68cm#

Volume of Cup A
#V=1/3pir^2h#
#V=1/3pi(15)^2(32)#
#V=2400pi#

Volume of Cup B
#V=1/3pir^2h#
#V=1/3pi(12)^2(12)#
#V=576pi#

Therefore, when Cup B is poured into Cup A, Cup A will not overflow

To find the height, we let #V=576pi# and using #r=15#

#V=576pi#
#1/3pir^2h=576pi#
#1/3pi(15)^2h=576pi#
#225/3h=576#
#h=7.68#