Cups A and B are cone shaped and have heights of #32 cm# and #15 cm# and openings with radii of #9 cm# and #3 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 · 2017-07-26T01:47:14

Cup A will not overflow

See below

The formula for the volume of a cone is #V=1/3*pi*r^2*h#

#V_A=1/3*pi*9^2*32" "=V_A=864pi" "=272.96cm^3#

#V_B=1/3*pi*3^2*15" "=V_A=45pi" "=141.30cm^3#

If cup B is full and its contents are poured into cup A, cup A will not overflow it will be #141.30/2712.96" "=0.052" "=5.2 %#