Question

Cups A and B are cone shaped and have heights of `27 cm` and `23 cm` and openings with radii of `7 cm` and `10 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:

The first step is to calculate the volumes ( V) of both cups.

`color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(V_("cone")=1/3pir^2h)color(white)(a/a)|)))`

`rArrV_(A)=1/3xxpixx7^2xx27=1156.327/3≈1385.44" cubic cm"`

`rArrV_(B)=1/3xxpixx10^2xx23=7225.663/3≈2408.55" cubic cm"`

Since `V_(B)>V_(A)" then cup A will overflow"`