Cups A and B are cone shaped and have heights of $32 cm$ and $12 cm$ and openings with radii of $18 cm$ and $6 cm$ , 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 · 2016-03-04T13:18:09

Find the volume of each one and compare them. Then, use cup's A volume on cup B and find the height.

Cup A will not overflow and height will be:

$h_A'=1,bar(333)cm$

The volume of a cone:

$V=1/3b*h$

where $b$ is the base and equal to $π*r^2$
$h$ is the height.

Cup A

$V_A=1/3b_A*h_A$

$V_A=1/3(π*18^2)*32$

$V_A=3456πcm^3$

Cup B

$V_B=1/3b_B*h_B$

$V_B=1/3(π*6^2)*12$

$V_B=144πcm^3$

Since $V_A>V_B$ the cup will not overflow. The new liquid volume of cup A after the pouring will be $V_A'=V_B$ :

$V_A'=1/3b_A*h_A'$

$V_B=1/3b_A*h_A'$

$h_A'=3(V_B)/b_A$

$h_A'=3(144π)/(π*18^2)$

$h_A'=1,bar(333)cm$

Cups A and B are cone shaped and have heights of 32 cm32 cm and 12 cm12 cm and openings with radii of 18 cm18 cm and 6 cm6 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?