Cups A and B are cone shaped and have heights of $35 c m$ $35 cm$ and $29 c m$ $29 cm$ and openings with radii of $14 c m$ $14 cm$ 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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Cups A and B are cone shaped and have heights of $35 c m$ $35 cm$ and $29 c m$ $29 cm$ and openings with radii of $14 c m$ $14 cm$ 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 · 2016-03-05T05:00:35

$V = \frac{1}{3} \cdot π \cdot r^{2} \cdot h$ $V = 1/3 * pi * r^2 * h$ Calculate the two volumes. If B is greater than A, it will overflow. If it is less, use the volume calculated to find the equivalent height of A.

Explanation:

$V_{A} = \frac{1}{3} \cdot π \cdot r_{A}^{2} \cdot h_{a}$ $V_A = 1/3 * pi * r_A^2 * h_a$
$V_{B} = \frac{1}{3} \cdot π \cdot r_{B}^{2} \cdot h_{b}$ $V_B = 1/3 * pi * r_B^2 * h_b$
$V_{B} = \frac{1}{3} \cdot π \cdot r_{A}^{2} \cdot h_{a}$ $V_B = 1/3 * pi * r_A^2 * h_a$ Solve for $h_{a}$ $h_a$

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Cups A and B are cone shaped and have heights of $35 c m$ $35 cm$ and $29 c m$ $29 cm$ and openings with radii of $14 c m$ $14 cm$ 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?

1 Answer

Explanation:

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Cups A and B are cone shaped and have heights of 35 cm35cm35 cm and 29 cm29cm29 cm and openings with radii of 14 cm14cm14 cm and 9 cm9cm9 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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Cups A and B are cone shaped and have heights of $35 c m$ $35 cm$ and $29 c m$ $29 cm$ and openings with radii of $14 c m$ $14 cm$ 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?