Question

Cups A and B are cone shaped and have heights of `27 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

`h = 8.03 cm`

Explanation:

The volume of a cone is found from `(pi r^2 h)/3`

The volumes of the two cones are:

A: `V = (pi xx6^2 xx 27)/3 = pi xx 36 xx 9 = 324 pi`

B: `V = (pi xx11^2 xx 24)/3 = pi xx 121 xx 8 = 968 pi`

We can see that the volume of B is much bigger than that of A, so if the contents of A when full, are poured into B, it will not overflow.

How high will B be filled? This asks for "h".

The volume poured into B is `324 pi " (the whole of A")`

`Vol = (pi r^2 h)/3`
`(pi 11^2h)/3 = 324 pi" divide by "`pi#

`h = (3 xx 324)/11^2`

`h = 8.03 cm`