Cups A and B are cone shaped and have heights of 27 cm27cm and 24 cm24cm and openings with radii of 6 cm6cm and 11 cm11cm, 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 cmh=8.03cm

Explanation:

The volume of a cone is found from (pi r^2 h)/3πr2h3

The volumes of the two cones are:

A: V = (pi xx6^2 xx 27)/3 = pi xx 36 xx 9 = 324 piV=π×62×273=π×36×9=324π

B: V = (pi xx11^2 xx 24)/3 = pi xx 121 xx 8 = 968 piV=π×112×243=π×121×8=968π

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")324π (the whole of A)

Vol = (pi r^2 h)/3Vol=πr2h3
(pi 11^2h)/3 = 324 pi" divide by " π112h3=324π divide by pi#

h = (3 xx 324)/11^2h=3×324112

h = 8.03 cmh=8.03cm