Cups A and B are cone shaped and have heights of #35 cm# and #29 cm# and openings with radii of #14 cm# and #16 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
May 19, 2016

cup A will overflow.


We need to calculate the volumes of both cups to begin with.

The volume (V) of a cone is found using the following formula.

where r is the radius and h the height of the cone.

cup A has r = 14 and h = 35

#rArrV_A=1/3pixx14^2xx35≈7183.78" cubic cm"#

cup B has r = 16 and h = 29

#rArrV_B=1/3pixx16^2xx29≈7774.39" cubic cm"#

volume of B > volume of A (7774.39 > 7183.78) and so when cup B is poured into cup A , it will overflow.