Cups A and B are cone shaped and have heights of #32 cm# and #24 cm# and openings with radii of #9 cm# and #5 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 · 2018-07-14T06:42:35

#7.41cm#

Volume of Cup A
#V=1/3pir^2h#
#V=1/3pitimes9^2times32#
#V=864pi#

Volume of Cup B
#V=1/3pir^2h#
#V=1/3pitimes5^2times24#
#V=200pi#

If Cup B was poured into Cup A, then Cup A will not overflow since it can hold a volume of #864pi#

To find the height of of water in Cup A,
#1/3pitimes9^2h=200pi#
#27pih=200pi#
#27h=200#
#h=200/27=7.41cm#