Cups A and B are cone shaped and have heights of $24 cm$ and $24 cm$ and openings with radii of $6 cm$ and $11 cm$ , 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?

Question

Cups A and B are cone shaped and have heights of $24 cm$ and $24 cm$ and openings with radii of $6 cm$ and $11 cm$ , 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

Impact of this question

1406 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-06T17:35:39

Cup A will overflow by $2135.2$ cub.cm

Explanation:

Let $V_A$ =Volume of cup A, $V_B$ = that of cup B
following the above notation, $r$ =radius, $h$ =height.

We know that Volume $V$ of a Cone $=(1/3)pir^2h.$

Since, $h_A=h_B=24, and r_B=11>r_A=6$ , we find that $V_B>V_A$ , so cup A will overflow by $V_B-V_A=1/3*pi*{r_B^2-r_A^2}*(h_A)=(1/3)pi(r_B+r_A)(r_B-r_A)*h_A=1/3*pi*17*5*24=680pi~=$ 2135.2cub.cm#

Science

Math

Humanities

... and beyond

Cups A and B are cone shaped and have heights of $24 cm$ and $24 cm$ and openings with radii of $6 cm$ and $11 cm$ , 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:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Cups A and B are cone shaped and have heights of 24 cm24 cm and 24 cm24 cm and openings with radii of 6 cm6 cm and 11 cm11 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:

Related questions

Impact of this question

Cups A and B are cone shaped and have heights of $24 cm$ and $24 cm$ and openings with radii of $6 cm$ and $11 cm$ , 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?