Cups A and B are cone shaped and have heights of 22 cm and 23 cm and openings with radii of 6 cm and 12 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
Tony B
Feb 22, 2016

color(brown)("Cone B has both a larger base diameter and greater height.")
color(brown)("So it is evident that it must have the larger volume. In")color(brown)("conclusion, cup A will overflow.")

Explanation:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Difference in volume demonstrated")

Volume of a cone is 1/3" base area "xx" height"

Cone A base area" " pir^2" "->" "pi6^2" "->" "36pi
Cone A height 22cm
=>"Volume cone A ="36pixx22 = 792pi cm^3
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cone B base area" " pir^2" "->" "pi12^2" "->" "144pi
Cone B height 23cm
=>"Volume cone B ="144pixx23=3312pi cm^3
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Clearly cup B has a significantly larger volume.

So as the question posed stands cup A will overflow.

color(green)("However, my experience of questions leads me to ask; should it be") color(green)("cup A that is bigger? Otherwise there is no point in even")color(green)("mentioning about height of fill level.")

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