Cups A and B are cone shaped and have heights of #32 cm# and #21 cm# and openings with radii of #15 cm# and #9 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 · 2018-07-14T04:23:57

Cup A will be filled to a height of #7.56cm#

Volume of Cup B
=#1/3pir^2h#
=#1/3pitimes9^2times21#
=#567pi#

Volume of Cup A
=#1/3pir^2h#
=#1/3pitimes15^2times32#
=#2400pi#

If Cup B is poured into Cup A, the cup will not overflow. To find the height of water in Cup A,

#1/3pitimes15^2h=567pi#

#(225h)/3=567#

#h=(567times3)/225#

#h=7.56#