Question

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?

Answer 1

cup A will overflow.

Explanation:

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

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(V=1/3pir^2h)color(white)(a/a)|)))`
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.