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?

1 Answer
Jun 11, 2016

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