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?

1 Answer
Jim G.
May 26, 2016

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.

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