Cups A and B are cone shaped and have heights of 32 cm and 12 cm and openings with radii of 15 cm and 12 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 31, 2018

Cup A will be filled to a height of 7.68cm

Explanation:

Volume of Cup A
V=1/3pir^2h
V=1/3pi(15)^2(32)
V=2400pi

Volume of Cup B
V=1/3pir^2h
V=1/3pi(12)^2(12)
V=576pi

Therefore, when Cup B is poured into Cup A, Cup A will not overflow

To find the height, we let V=576pi and using r=15

V=576pi
1/3pir^2h=576pi
1/3pi(15)^2h=576pi
225/3h=576
h=7.68