Cups A and B are cone shaped and have heights of #32 cm# and #12 cm# and openings with radii of #5 cm# and #8 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 · 2016-02-22T05:25:19

When cup B is full and its contents are poured into cup A, cup A will not overflow. It will be filled up to a height of #30.72# cm

Volume of a cone whose radius is #r# and height is #h# is given by #1/3pir^2h#.

Hence volume of Cup A is #1/3pi5^2*32# = #(25*32)/3pi# = #800/3pi#
and volume of Cup B is #1/3pi8^(2)*12# = #(64*12)/3pi# = #768/3pi#.

As volume of Cup B is less than that of A, when cup B is full and its contents are poured into cup A, cup A will not overflow.

Let Cup A be filled till height #a#, than #1/3pi5^2*a# = #768/3pi#

or #25a=768# or #a=768/25= 30.72# cm