Question

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?

Answer 1

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.