Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $12 c m$ $12 cm$ and openings with radii of $15 c m$ $15 cm$ 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 $32 c m$ $32 cm$ and $12 c m$ $12 cm$ and openings with radii of $15 c m$ $15 cm$ 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 · 2018-07-31T08:59:06

Cup A will be filled to a height of $7.68 c m$ $7.68cm$

Explanation:

Volume of Cup A
$V = \frac{1}{3} π r^{2} h$ $V=1/3pir^2h$
$V = \frac{1}{3} π {(15)}^{2} (32)$ $V=1/3pi(15)^2(32)$
$V = 2400 π$ $V=2400pi$

Volume of Cup B
$V = \frac{1}{3} π r^{2} h$ $V=1/3pir^2h$
$V = \frac{1}{3} π {(12)}^{2} (12)$ $V=1/3pi(12)^2(12)$
$V = 576 π$ $V=576pi$

Therefore, when Cup B is poured into Cup A, Cup A will not overflow

To find the height, we let $V = 576 π$ $V=576pi$ and using $r = 15$ $r=15$

$V = 576 π$ $V=576pi$
$\frac{1}{3} π r^{2} h = 576 π$ $1/3pir^2h=576pi$
$\frac{1}{3} π {(15)}^{2} h = 576 π$ $1/3pi(15)^2h=576pi$
$\frac{225}{3} h = 576$ $225/3h=576$
$h = 7.68$ $h=7.68$

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Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $12 c m$ $12 cm$ and openings with radii of $15 c m$ $15 cm$ 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?

1 Answer

Explanation:

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Cups A and B are cone shaped and have heights of 32 cm32cm32 cm and 12 cm12cm12 cm and openings with radii of 15 cm15cm15 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 $32 c m$ $32 cm$ and $12 c m$ $12 cm$ and openings with radii of $15 c m$ $15 cm$ 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?