Question

Cups A and B are cone shaped and have heights of `35 cm` and `24 cm` and openings with radii of `9 cm` and `11 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 overflow

Explanation:

The volume (`V_A`) of cone cup-A with vertical height `35` cm & radius `9` cm is

`V_A=1/3\pi r^2h=1/3\pi(9^2)(35)=945\pi\ cm^3`

The volume (`V_B`) of cone cup-B with vertical height `24` cm & radius `11` cm is

`V_B=1/3\pi r^2h=1/3\pi(11^2)(24)=968\pi\ cm^3`

Since, the volume of cone cup B is more than that of cone cup A

`V_B>V_A`

hence when the content of full cup B is poured into cup A, cup A would overflow.