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?

1 Answer
Dec 24, 2016

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.