Question

Cups A and B are cone shaped and have heights of `32 cm` and `33 cm` and openings with radii of `16 cm` and `17 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?

Answer 1

Cone B has a greater volume than cone A, so if its contents are all poured into A, it will overflow.

Explanation:

Volume of cone A`=1/3pir^2h`
A`=1/3 pi*16^2*32`
`=1/3*3.141592654*256*32`
`=1/3*25735.927`
`=25735.927/3`
Vol. A`=8578.642cm^3`

Vol. B`=1/3pi*17^2*33`
`=1/3*3.14159254*289*33`
`=1/3*29961.369`
`=29961.369/3`
Vol. B`=9987.123cm^3`

Cone B has a greater volume than cone A, so if its contents are all poured into A, it will overflow.

`9987.123cm^3-8578.642cm^3 = 1408.481cm^3` will be left in B if A is filled from the contents of B.