Cups A and B are cone shaped and have heights of $29 cm$ and $33 cm$ and openings with radii of $7 cm$ 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?

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Answer 1 · 2018-07-30T00:17:34

Cup A will overflow

Volume of a cone $= 1/3 pi r^2h$

$V_A = 1/3*(7^2)*29 " cc"$

$= 473.667 " cc"$

$V_B = 1/3*(12^2)*33 " cc"$

$= 1584 " cc"$

Cup B holds 1110.333 cc more than cup A so cup A will overflow.

Note:
cc $=$ cubic centimeters.
$1"cc" = 1ml$

Cups A and B are cone shaped and have heights of 29 cm29 cm and 33 cm33 cm and openings with radii of 7 cm7 cm and 12 cm12 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?