Cups A and B are cone shaped and have heights of #35 cm# and #29 cm# and openings with radii of #12 cm# and #16 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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Cups A and B are cone shaped and have heights of #35 cm# and #29 cm# and openings with radii of #12 cm# and #16 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 · 2016-08-08T13:08:51

#=31.42 cm#

Explanation:

Volume of Cup #A=pir^2(h/3)# where #r=12 cm# and #h=35 cm#
#=pi(12^2)(35/3)=1680pi#
Volume of Cup #B=pir^2(h/3)# where #r=16 cm# and #h=29 cm#
#=pi(16^2)(29/3)=1508pi#
Since volume of #B# is less than volume of #A# it will not overflow
Now we can write
#pi(12)^2(H/3)=1508pi#
or
#H=4524/144=31.42 cm#
where #H# is the height of Cup #A# will be filled.

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Cups A and B are cone shaped and have heights of #35 cm# and #29 cm# and openings with radii of #12 cm# and #16 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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Explanation:

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