Cups A and B are cone shaped and have heights of 33 cm and 37 cm and openings with radii of 12 cm and 7 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
Solace M.
Sep 17, 2017

No, it will only be filled ~~73.4% of the way

Explanation:

The formula for volume of a cone is V=pir^2 h/3, where r is the radius and h is the height of the cone. For Cup A, r=33 and h=12. Plug that into the formula and you get
V=pi33^2 * 12/3
V=1089pi * 4
V=4356pi

For Cup B, r=37 and h=7. Plug that into the formula and you get
V=pi37^2 * 7/3
V=1369pi *7/3
V=(9583pi)/3
V~~3194.3pi

As you can see, Cup A has a bigger volume then Cup B, since 4356>3194.3, therefor Cup A will not overflow when Cup B is pored into it. As for how high the contents will reach in Cup A, you simply divide Cup B's volume by Cup A's volume to get
(4356pi)/(3194.3pi)=9583/13068~~73.4%

I hope I helped!

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