Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $24 c m$ $24 cm$ and openings with radii of $9 c m$ $9 cm$ and $5 c m$ $5 cm$ , 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 $24 c m$ $24 cm$ and openings with radii of $9 c m$ $9 cm$ and $5 c m$ $5 cm$ , 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 · 2018-07-14T06:42:35

$7.41 c m$ $7.41cm$

Explanation:

Volume of Cup A
$V = \frac{1}{3} π r^{2} h$ $V=1/3pir^2h$
$V = \frac{1}{3} π \times 9^{2} \times 32$ $V=1/3pitimes9^2times32$
$V = 864 π$ $V=864pi$

Volume of Cup B
$V = \frac{1}{3} π r^{2} h$ $V=1/3pir^2h$
$V = \frac{1}{3} π \times 5^{2} \times 24$ $V=1/3pitimes5^2times24$
$V = 200 π$ $V=200pi$

If Cup B was poured into Cup A, then Cup A will not overflow since it can hold a volume of $864 π$ $864pi$

To find the height of of water in Cup A,
$\frac{1}{3} π \times 9^{2} h = 200 π$ $1/3pitimes9^2h=200pi$
$27 π h = 200 π$ $27pih=200pi$
$27 h = 200$ $27h=200$
$h = \frac{200}{27} = 7.41 c m$ $h=200/27=7.41cm$

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Cups A and B are cone shaped and have heights of $32 c m$ $32 cm$ and $24 c m$ $24 cm$ and openings with radii of $9 c m$ $9 cm$ and $5 c m$ $5 cm$ , 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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Science

Math

Humanities

... and beyond

Cups A and B are cone shaped and have heights of 32cm32 cm and 24cm24 cm and openings with radii of 9cm9 cm and 5cm5 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 $32 c m$ $32 cm$ and $24 c m$ $24 cm$ and openings with radii of $9 c m$ $9 cm$ and $5 c m$ $5 cm$ , 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?