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?

1 Answer
Mar 4, 2016

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

Explanation:

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