Cups A and B are cone shaped and have heights of $27 cm$ and $23 cm$ and openings with radii of $7 cm$ and $10 cm$ , 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 $27 cm$ and $23 cm$ and openings with radii of $7 cm$ and $10 cm$ , 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

1390 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-29T19:49:39

cup A will overflow.

Explanation:

The first step is to calculate the volumes ( V) of both cups.

$color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(V_("cone")=1/3pir^2h)color(white)(a/a)|)))$

$rArrV_(A)=1/3xxpixx7^2xx27=1156.327/3≈1385.44" cubic cm"$

$rArrV_(B)=1/3xxpixx10^2xx23=7225.663/3≈2408.55" cubic cm"$

Since $V_(B)>V_(A)" then cup A will overflow"$

Science

Math

Humanities

... and beyond

Cups A and B are cone shaped and have heights of $27 cm$ and $23 cm$ and openings with radii of $7 cm$ and $10 cm$ , 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 27 cm27 cm and 23 cm23 cm and openings with radii of 7 cm7 cm and 10 cm10 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 $27 cm$ and $23 cm$ and openings with radii of $7 cm$ and $10 cm$ , 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?