Question

Cups A and B are cone shaped and have heights of `28 cm` and `23 cm` and openings with radii of `6 cm` and `9 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 here is to calculate the volume (V) of the 2 cups using

`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.

• If `V_B>V_A,"then cup A will overflow"`

`V_A=1/3xxpixx6^2xx28≈1055.575" cubic cm"`

`V_B=1/3xxpixx9^2xx23≈1950.929" cubic cm"`

Since 1950.929 > 1055.575 , then cup A will overflow.