Cups A and B are cone shaped and have heights of 27 cm27cm and 25 cm25cm and openings with radii of 7 cm7cm and 9 cm9cm, 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
Nov 19, 2017

Yes, cup A will overflow.

Explanation:

Find the volume of each cone by using the following formula:
V=pir^2(h/3)V=πr2(h3)

V_A=pi49(27/3)=441picm^3VA=π49(273)=441πcm3
V_B=pi81(25/3)=675picm^3VB=π81(253)=675πcm3

Since cone B has a greater volume than cone A, and it is given that cone B is completely full, it can be concluded that cup A will overflow.