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?

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Answer 1 · 2016-06-11T14:36:16

$h = 8.03 cm$

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#

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

$h = 8.03 cm$

Cups A and B are cone shaped and have heights of 27 cm27 cm and 24 cm24 cm and openings with radii of 6 cm6 cm and 11 cm11 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?