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?

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Answer 1 · 2016-12-24T17:24:37

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

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.

Cups A and B are cone shaped and have heights of 32 cm32 cm and 33 cm33 cm and openings with radii of 16 cm16 cm and 17 cm17 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?