Cups A and B are cone shaped and have heights of #24 cm# and #23 cm# and openings with radii of #11 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?

1 Answer
Shwetank Mauria · P dilip_k
Mar 12, 2016

#~~20.7cm#

Explanation:

Volume of a cone is given by #1/3pir^2h#, hence

Volume of cone A is #1/3pi11^2*24=8*11^2pi=968pi# and

Volume of cone B is #1/3pi9^2*23=27*23pi=621pi#
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It is obvious that when contents of a full cone B are poured into cone A, it will not overflow. Let it reach where upper circular surface will form a circle of radius #x# and will reach a height of #y#,
then the relation becomes
#x/11=y/24=>x=(11y)/24#
So equating #1/3pix^2y=621pi#
#=>1/3pi((11y)/24)^2y=621pi#
#=>y^3=(621*3*24^2)/11^2~~20.7cm#

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