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