Question

Cups A and B are cone shaped and have heights of `32 cm` and `37 cm` and openings with radii of `16 cm` and `17 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

If contents of cup `B` filled fully, is poured into cup `A`, cup `A` will overflow.

Explanation:

Let `V_1` and `V_2` denote the volume of cups `A & B` resp.

Let `r`=radii, `h`=heights.

Volume `V` of a cone is `V=1/3pir^2h.`

Hence, `V_1=1/3*pi*16^2*32` and, `V_2=1/3*pi*17^2*37.`

Since, `17^2>16^2, &, 37>32`, evidently `V_2>V_1`.

Hence, if contents of cup `B` filled fully, is poured into cup `A`, cup `A` will overflow.