Question

Cups A and B are cone shaped and have heights of `32 cm` and `27 cm` and openings with radii of `12 cm` and `12 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

`color(blue)(27cm)`

Explanation:

Volume of a cone is given as:

`1/3"area of base"xx "height"`

We can see that both have the same radii, but A has a greater height, so A has a greater volume than B.

Volume of A:

`1/3pi(144)(32)=1536pi`

Volume of B:

`1/3pi(144)(27)=1296pi`

Volume of partly filled A is equal to the volume of B:

`1/3pi(144)*h=1296pi`

`h=(3*1296pi)/(144pi)=27cm`

Well that's no surprise, since they both have the same radius. I would think this part of the question is incorrect.