Cups A and B are cone shaped and have heights of $33 c m$ $33 cm$ and $23 c m$ $23 cm$ and openings with radii of $14 c m$ $14 cm$ and $7 c m$ $7 cm$ , 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 $33 c m$ $33 cm$ and $23 c m$ $23 cm$ and openings with radii of $14 c m$ $14 cm$ and $7 c m$ $7 cm$ , 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 · 2018-07-26T07:44:05

Cup A will be filled to a height of $5.75 c m$ $5.75cm$

Explanation:

Volume of Cup B
$v = π r^{2} h$ $v=pir^2h$
$= π {(7)}^{2} \times 23$ $=pi(7)^2times23$
$v = 1127 π$ $v=1127pi$

Volume of Cup A
$v = π r^{2} h$ $v=pir^2h$
$= π {(14)}^{2} \times 33$ $=pi(14)^2times33$
$v = 6468 π$ $v=6468pi$

Therefore, Cup A will not overflow if the volume of Cup B is poured into A

To find the height reached in Cup A, we can use what we already know --> $r = 14$ $r=14$ and $v = 1127 π$ $v=1127pi$
$v = π r^{2} h$ $v=pir^2h$
$1127 π = π {(14)}^{2} h$ $1127pi=pi(14)^2h$
$1127 = 196 h$ $1127=196h$
$h = \frac{1127}{196}$ $h=1127/196$
$h = 5.75 c m$ $h=5.75cm$

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Cups A and B are cone shaped and have heights of $33 c m$ $33 cm$ and $23 c m$ $23 cm$ and openings with radii of $14 c m$ $14 cm$ and $7 c m$ $7 cm$ , 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 33cm33 cm and 23cm23 cm and openings with radii of 14cm14 cm and 7cm7 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 $33 c m$ $33 cm$ and $23 c m$ $23 cm$ and openings with radii of $14 c m$ $14 cm$ and $7 c m$ $7 cm$ , 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?