Cups A and B are cone shaped and have heights of #32 cm# and #27 cm# and openings with radii of #12 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?

Question

1690 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-24T13:26:52

#color(blue)(27cm)#

Volume of a cone is given as:

#1/3"area of base"xx "height"#

We can see that both have the same radii, but A has a greater height, so A has a greater volume than B.

Volume of A:

#1/3pi(144)(32)=1536pi#

Volume of B:

#1/3pi(144)(27)=1296pi#

Volume of partly filled A is equal to the volume of B:

#1/3pi(144)*h=1296pi#

#h=(3*1296pi)/(144pi)=27cm#

Well that's no surprise, since they both have the same radius. I would think this part of the question is incorrect.