Cups A and B are cone shaped and have heights of $28 c m$ $28 cm$ and $23 c m$ $23 cm$ and openings with radii of $6 c m$ $6 cm$ and $12 c m$ $12 cm$ , 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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Cups A and B are cone shaped and have heights of $28 c m$ $28 cm$ and $23 c m$ $23 cm$ and openings with radii of $6 c m$ $6 cm$ and $12 c m$ $12 cm$ , 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 · 2016-03-08T10:41:37

cup A will overflow.

Explanation:

Volume (V) of cone = $\frac{1}{3} π r^{2} h$ $1/3pir^2h$
where h represents height and r , the radius.

$V_{A} = \frac{1}{3} π \times 6^{2} \times 28 = 336 π \approx 1055.575 cubic cm$ $V_A = 1/3pixx6^2xx28 = 336pi ≈ 1055.575 " cubic cm "$

and $V_{B} = \frac{1}{3} π \times 12^{2} \times 23 = 1104 π \approx 3468.318 cubic cm$ $V_B = 1/3pixx12^2xx23 = 1104pi ≈ 3468.318 " cubic cm "$

since $V_{B} > V_{A} cup A will overflow$ $V_B > V_A " cup A will overflow "$

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Cups A and B are cone shaped and have heights of $28 c m$ $28 cm$ and $23 c m$ $23 cm$ and openings with radii of $6 c m$ $6 cm$ and $12 c m$ $12 cm$ , 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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Explanation:

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Cups A and B are cone shaped and have heights of 28 cm28cm28 cm and 23 cm23cm23 cm and openings with radii of 6 cm6cm6 cm and 12 cm12cm12 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 $28 c m$ $28 cm$ and $23 c m$ $23 cm$ and openings with radii of $6 c m$ $6 cm$ and $12 c m$ $12 cm$ , 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?