Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $25 c m$ $25 cm$ and openings with radii of $7 c m$ $7 cm$ and $9 c m$ $9 cm$ , 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 · 2017-11-19T17:03:21

Yes, cup A will overflow.

Find the volume of each cone by using the following formula:
$V = π r^{2} (\frac{h}{3})$ $V=pir^2(h/3)$

$V_{A} = π 49 (\frac{27}{3}) = 441 π c m^{3}$ $V_A=pi49(27/3)=441picm^3$
$V_{B} = π 81 (\frac{25}{3}) = 675 π c m^{3}$ $V_B=pi81(25/3)=675picm^3$

Since cone B has a greater volume than cone A, and it is given that cone B is completely full, it can be concluded that cup A will overflow.

Cups A and B are cone shaped and have heights of 27cm27 cm and 25cm25 cm and openings with radii of 7cm7 cm and 9cm9 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?