Question

Cups A and B are cone shaped and have heights of `24 cm` and `24 cm` and openings with radii of `6 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 by `2135.2` cub.cm

Explanation:

Let `V_A`=Volume of cup A, `V_B`= that of cup B
following the above notation, `r`=radius, `h`=height.

We know that Volume `V` of a Cone`=(1/3)pir^2h.`

Since, `h_A=h_B=24, and r_B=11>r_A=6`, we find that `V_B>V_A`, so cup A will overflow by `V_B-V_A=1/3*pi*{r_B^2-r_A^2}*(h_A)=(1/3)pi(r_B+r_A)(r_B-r_A)*h_A=1/3*pi*17*5*24=680pi~=`2135.2cub.cm#