Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $6 c m$ $6 cm$ and $11 c m$ $11 cm$ , 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

$h = 8.03 c m$ $h = 8.03 cm$

The volume of a cone is found from $\frac{π r^{2} h}{3}$ $(pi r^2 h)/3$

The volumes of the two cones are:

A: $V = \frac{π \times 6^{2} \times 27}{3} = π \times 36 \times 9 = 324 π$ $V = (pi xx6^2 xx 27)/3 = pi xx 36 xx 9 = 324 pi$

B: $V = \frac{π \times 11^{2} \times 24}{3} = π \times 121 \times 8 = 968 π$ $V = (pi xx11^2 xx 24)/3 = pi xx 121 xx 8 = 968 pi$

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 $324 π (the whole of A)$ $324 pi " (the whole of A")$

$V o l = \frac{π r^{2} h}{3}$ $Vol = (pi r^2 h)/3$
$\frac{π 11^{2} h}{3} = 324 π divide by$ $(pi 11^2h)/3 = 324 pi" divide by "$ pi#

$h = \frac{3 \times 324}{11^{2}}$ $h = (3 xx 324)/11^2$

$h = 8.03 c m$ $h = 8.03 cm$

Cups A and B are cone shaped and have heights of 27 cm27cm27 cm and 24 cm24cm24 cm and openings with radii of 6 cm6cm6 cm and 11 cm11cm11 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?