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
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