Cups A and B are cone shaped and have heights of 32 cm32cm and 27 cm27cm and openings with radii of 12 cm12cm and 12 cm12cm, 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
May 24, 2018

color(blue)(27cm)27cm

Explanation:

Volume of a cone is given as:

1/3"area of base"xx "height"13area of base×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)=1536pi13π(144)(32)=1536π

Volume of B:

1/3pi(144)(27)=1296pi13π(144)(27)=1296π

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

1/3pi(144)*h=1296pi13π(144)h=1296π

h=(3*1296pi)/(144pi)=27cmh=31296π144π=27cm

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