Cups A and B are cone shaped and have heights of $38 cm$ and $25 cm$ and openings with radii of $8 cm$ and $13 cm$ , 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 · 2016-02-22T17:50:32

Cup A will overflow. The exceeding volume is $(1793pi)/3 ~=1,877.63cm^3$

Finding the maximum volume of A and B

$V_A=(S_(base A)*height_A)/3=(pi*r_A^2*h_A)/3=(pi*8^2*38)/3=(2432pi)/3$

$V_B=(S_(base B)*height_B)/3=(pi*r_B^2*h_B)/3=(pi*13^2*25)=(4225pi)/3$

Since $V_A < V_B$ , cup A will overflow and

$Delta V=V_B-V_A=(4225pi)/3-(2432pi)/3=(1793pi)/3~=1,877.63cm^3$

Cups A and B are cone shaped and have heights of 38 cm38 cm and 25 cm25 cm and openings with radii of 8 cm8 cm and 13 cm13 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?