Cups A and B are cone shaped and have heights of $33 cm$ and $29 cm$ and openings with radii of $10 cm$ and $13 cm$ , 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 · 2018-07-03T03:47:55

Yes, cup A will overflow.

Given: cup A is a cone with $r = 10 cm; h = 33 cm$
$" "$ cup B is a cone with $r = 13 cm; h = 29 cm$

Volume of a circular right cone: $V = 1/3 pi r^2 h$

$V_b = 1/3 pi 13^2 * 29 = 4901/3 pi ~~ 5132 " "cm^3$

$V_a = 1/3 pi 10^2 * 33 = 1100 pi ~~ 3456 " "cm^3$

Cups A and B are cone shaped and have heights of 33 cm33 cm and 29 cm29 cm and openings with radii of 10 cm10 cm and 13 cm13 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?