Cups A and B are cone shaped and have heights of $38 c m$ $38 cm$ and $25 c m$ $25 cm$ and openings with radii of $8 c m$ $8 cm$ and $13 c m$ $13 cm$ , 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 $38 c m$ $38 cm$ and $25 c m$ $25 cm$ and openings with radii of $8 c m$ $8 cm$ and $13 c m$ $13 cm$ , 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 · 2016-02-22T17:50:32

Cup A will overflow. The exceeding volume is $\frac{1793 π}{3} ≅ 1, 877.63 c m^{3}$ $(1793pi)/3 ~=1,877.63cm^3$

Explanation:

Finding the maximum volume of A and B

$V_{A} = \frac{S_{b a s e A} \cdot h e i g h t_{A}}{3} = \frac{π \cdot r_{A}^{2} \cdot h_{A}}{3} = \frac{π \cdot 8^{2} \cdot 38}{3} = \frac{2432 π}{3}$ $V_A=(S_(base A)*height_A)/3=(pi*r_A^2*h_A)/3=(pi*8^2*38)/3=(2432pi)/3$

$V_{B} = \frac{S_{b a s e B} \cdot h e i g h t_{B}}{3} = \frac{π \cdot r_{B}^{2} \cdot h_{B}}{3} = (π \cdot 13^{2} \cdot 25) = \frac{4225 π}{3}$ $V_B=(S_(base B)*height_B)/3=(pi*r_B^2*h_B)/3=(pi*13^2*25)=(4225pi)/3$

Since $V_{A} < V_{B}$ $V_A < V_B$ , cup A will overflow and

$Delta V=V_B-V_A=(4225pi)/3-(2432pi)/3=(1793pi)/3~=1,877.63cm^3$

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Cups A and B are cone shaped and have heights of $38 c m$ $38 cm$ and $25 c m$ $25 cm$ and openings with radii of $8 c m$ $8 cm$ and $13 c m$ $13 cm$ , 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 38 cm38cm38 cm and 25 cm25cm25 cm and openings with radii of 8 cm8cm8 cm and 13 cm13cm13 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 $38 c m$ $38 cm$ and $25 c m$ $25 cm$ and openings with radii of $8 c m$ $8 cm$ and $13 c m$ $13 cm$ , 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?