Cups A and B are cone shaped and have heights of #33 cm# and #23 cm# and openings with radii of #14 cm# and #7 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
Jul 26, 2018

Cup A will be filled to a height of #5.75cm#

Explanation:

Volume of Cup B
#v=pir^2h#
#=pi(7)^2times23#
#v=1127pi#

Volume of Cup A
#v=pir^2h#
#=pi(14)^2times33#
#v=6468pi#

Therefore, Cup A will not overflow if the volume of Cup B is poured into A

To find the height reached in Cup A, we can use what we already know --> #r=14# and #v=1127pi#
#v=pir^2h#
#1127pi=pi(14)^2h#
#1127=196h#
#h=1127/196#
#h=5.75cm#