Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $37 c m$ $37 cm$ and openings with radii of $16 c m$ $16 cm$ and $19 c m$ $19 cm$ , 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 $32 c m$ $32 cm$ and $37 c m$ $37 cm$ and openings with radii of $16 c m$ $16 cm$ and $19 c m$ $19 cm$ , 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 · 2016-03-14T19:15:33

overflow

Explanation:

The volume of a cone is calculated using:

$V = \frac{1}{3} π r^{2} h r is radius and h , the height$ $V = 1/3pir^2h" r is radius and h , the height "$

calculate volume of both cones and compare

$V_{A} = \frac{1}{3} π \times 16^{2} \times 32 \approx 8578.64 cubic cm$ $V_A = 1/3pixx16^2xx32 ≈ 8578.64" cubic cm "$

$V_{B} = \frac{1}{3} π \times 19^{2} \times 37 \approx 13987.42 cubic cm$ $V_B = 1/3pixx19^2xx37 ≈ 13987.42" cubic cm "$

Since $V_{B} > V_{A} when poured into A it will overflow$ $V_B > V_A " when poured into A it will overflow "$

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Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $37 c m$ $37 cm$ and openings with radii of $16 c m$ $16 cm$ and $19 c m$ $19 cm$ , 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 32 cm32cm32 cm and 37 cm37cm37 cm and openings with radii of 16 cm16cm16 cm and 19 cm19cm19 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 $32 c m$ $32 cm$ and $37 c m$ $37 cm$ and openings with radii of $16 c m$ $16 cm$ and $19 c m$ $19 cm$ , 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?