Cups A and B are cone shaped and have heights of $34 c m$ $34 cm$ and $23 c m$ $23 cm$ and openings with radii of $15 c m$ $15 cm$ and $17 c m$ $17 cm$ , 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 $34 c m$ $34 cm$ and $23 c m$ $23 cm$ and openings with radii of $15 c m$ $15 cm$ and $17 c m$ $17 cm$ , 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 · 2018-01-14T11:40:29

$32.44$ $32.44$ cm high in cup "A" will be filled.

Explanation:

Cup B (Conical): radius and height are $r_{b} = 17 c m; h_{b} = 23 c m$ $r_b=17 cm ; h_b =23 cm$

Capcaity of Cup B is $V_{b} = \frac{1}{3} \cdot π \cdot r_{b}^{2} \cdot h_{b}$ $V_b=1/3*pi*r_b^2*h_b$

$V_{b} = \frac{1}{3} \cdot π \cdot 17^{2} \cdot 23 = 6960.72$ $V_b=1/3*pi*17^2*23 =6960.72$ cubic cm

Cup A (Conical): radius and height are $r_{a} = 15 c m; h_{a} = 34 c m$ $r_a=15 cm ; h_a =34 cm$

Capcaity of Cup A is $V_{a} = \frac{1}{3} \cdot π \cdot r_{a}^{2} \cdot h_{a}$ $V_a=1/3*pi*r_a^2*h_a$

$V_{a} = \frac{1}{3} \cdot π \cdot 15^{2} \cdot 34 = 8011.06$ $V_a=1/3*pi*15^2*34 =8011.06$ cubic cm

$\frac{r_{a}}{h_{a}} = \frac{15}{34}$ $r_a/h_a=15/34$ . Since the capacity of cup B is less than that of

cup A , the content will not overflow. Let the height and radius in

the content cone in cup A be $h_{2} and r_{2}$ $h_2 and r_2$

$\frac{r_{2}}{h_{2}} = \frac{15}{34}; r_{2} = \frac{15}{34} \cdot h_{2}; V_{c} = 6960.72; V_{c}$ $r_2/h_2=15/34 ; r_2= 15/34*h_2 ; V_c=6960.72 ; V_c$ is the

volume of contents in cup A $:. 1/3*pi*r_2^2*h_2 =6960.72$

$r_2^2*h_2 =(6960.72*3)/pi$ or

$(15/34*h_2)^2*h_2=(6960.72*3)/pi$ or

$h^3=(6960.72*3)/pi*34^2/15^2=34150.8$

$:. h=root(3) 34150.8 ~~32.44(2dp)$ cm .

$32.44$ cm high in cup "A" will be filled. [Ans]

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Cups A and B are cone shaped and have heights of $34 c m$ $34 cm$ and $23 c m$ $23 cm$ and openings with radii of $15 c m$ $15 cm$ and $17 c m$ $17 cm$ , 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 34 cm34cm34 cm and 23 cm23cm23 cm and openings with radii of 15 cm15cm15 cm and 17 cm17cm17 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 $34 c m$ $34 cm$ and $23 c m$ $23 cm$ and openings with radii of $15 c m$ $15 cm$ and $17 c m$ $17 cm$ , 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?