Cups A and B are cone shaped and have heights of 32 cm32cm and 12 cm12cm and openings with radii of 15 cm15cm and 12 cm12cm, 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 7.68cm7.68cm

Explanation:

Volume of Cup A
V=1/3pir^2hV=13πr2h
V=1/3pi(15)^2(32)V=13π(15)2(32)
V=2400piV=2400π

Volume of Cup B
V=1/3pir^2hV=13πr2h
V=1/3pi(12)^2(12)V=13π(12)2(12)
V=576piV=576π

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

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

V=576piV=576π
1/3pir^2h=576pi13πr2h=576π
1/3pi(15)^2h=576pi13π(15)2h=576π
225/3h=5762253h=576
h=7.68h=7.68