Question

Cups A and B are cone shaped and have heights of `20 cm` and `12 cm` and openings with radii of `5 cm` and `3 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 `4.32 cm`

Explanation:

Volume of cup `A=pir^2h`
`=pi(5)^2(20)`
`=500pi`

Volume of cup `B=pir^2h`
`=pi(3)^2(12)`
`=108pi`
So
`pir^2H=108pi`
or
`r^2H=108`
or
`5^2H=108`
or
`25H=108`
or
`H=108/25`
`H=4.32`
So cup A will be filled to a height of `4.32 cm`