Cups A and B are cone shaped and have heights of 27 cm and 21 cm and openings with radii of 7 cm and 11 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
Aug 20, 2016

cup A will overflow.

Explanation:

We require to compare the color(blue)"volumes" of the 2 cups.

The color(blue)"volume(V) of a cone " is

color(orange)"Reminder " 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, is the height.

rArrV_(A)=(pixx7^2xx27)/3≈1385.442" cubic cm"

and V_(B)=(pixx11^2xx21)/3≈2660.293" cubic cm"

Since volume of cup B > volume of cup A, when the contents of B are poured into A, it will overflow.