Cups A and B are cone shaped and have heights of $24 c m$ $24 cm$ and $21 c m$ $21 cm$ and openings with radii of $8 c m$ $8 cm$ and $11 c m$ $11 cm$ , 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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Cups A and B are cone shaped and have heights of $24 c m$ $24 cm$ and $21 c m$ $21 cm$ and openings with radii of $8 c m$ $8 cm$ and $11 c m$ $11 cm$ , 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 · 2018-01-09T19:34:54

Cone A will overflow because it has a volume 1052.434 $c m^{3}$ $cm^3$ lower than Cone B.

Explanation:

First, find the volume of both cones using the equation $V = π r^{2} \frac{h}{3}$ $V = pir^2h/3$
V - Volume
r - radius
h - height

Cone A - $V = π {(8)}^{2} \frac{24}{3} \approx 1608.495 c m^{3}$ $V = pi(8)^2(24)/3 ~~ 1608.495cm^3$
Cone B - $V = π {(11)}^{2} \frac{21}{3} \approx 2660.929 c m^{3}$ $V = pi(11)^2(21)/3 ~~ 2660.929cm^3$

Cone B has a greater volume. Therefore, Cone A will overflow in the scenario presented.

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Cups A and B are cone shaped and have heights of $24 c m$ $24 cm$ and $21 c m$ $21 cm$ and openings with radii of $8 c m$ $8 cm$ and $11 c m$ $11 cm$ , 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

Explanation:

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Science

Math

Humanities

... and beyond

Cups A and B are cone shaped and have heights of 24cm24 cm and 21cm21 cm and openings with radii of 8cm8 cm and 11cm11 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

Explanation:

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Impact of this question

Cups A and B are cone shaped and have heights of $24 c m$ $24 cm$ and $21 c m$ $21 cm$ and openings with radii of $8 c m$ $8 cm$ and $11 c m$ $11 cm$ , 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?