Question

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?

Answer 1

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`