Question

Cups A and B are cone shaped and have heights of `39 cm` and `22 cm` and openings with radii of `17 cm` and `13 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 not overflow.
`Height=12.865` cm

Explanation:

Total volume of cup `B=pir^2h/3=pi(13)^2(22/3)=1239.33pi`
Total volume of cup `A=pir^2h/3=pi(17)^2(39/3)=3757pi`
Since volume of cup `B` is less than volume of cup `A`; Contents of cup `B` if poured into cup `A` will not make cup `A` overflow
hence cup `A` will not overflow.

So we have to find `H=?` the height in Cup `A` which will have content of same volume as volume of Cup`B`

`pi(17)^2(H/3)=1239.33pi`
or

`H/3=1239.33/17^2=4.288`
or

`H=12.865` cm