Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $5 c m$ $5 cm$ and $14 c m$ $14 cm$ , 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 $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $5 c m$ $5 cm$ and $14 c m$ $14 cm$ , 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 · 2016-08-24T07:43:28

A will overflow.

Explanation:

Remember that: $V_{cone} = \frac{π r^{2} h}{3}$ $V_"cone" = (pi r^2h)/3$

$V_{A} = \frac{π \times 5^{2} \times 27}{3} and V_{B} = \frac{π \times 14^{2} \times 24}{3}$ $V_A = (pixx 5^2xx27)/3 and V_B= (pi xx14^2xx24)/3$

We do not need the actual volumes, we just need to know which one is greater. $π and 3$ $pi and 3$ are common to bother and therefore can be ignored in the comparison.

$A : 5^{2} \times 27 = 675 and B : 14^{2} \times 24 = 4, 704$ $A: 5^2 xx27 = 675 " "and " "B: 14^2 xx24 = 4,704$

The volume of B is significantly bigger than A.
A will overflow (several times if A is emptied between fills)

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Cups A and B are cone shaped and have heights of $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $5 c m$ $5 cm$ and $14 c m$ $14 cm$ , 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 27cm27 cm and 24cm24 cm and openings with radii of 5cm5 cm and 14cm14 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 $27 c m$ $27 cm$ and $24 c m$ $24 cm$ and openings with radii of $5 c m$ $5 cm$ and $14 c m$ $14 cm$ , 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?