Cups A and B are cone shaped and have heights of $35 cm$ and $23 cm$ and openings with radii of $14 cm$ and $7 cm$ , 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 · 2017-04-09T10:19:28

6 cm

Volume of a cone = $pir^2h/3$
where r = radius of the base, and h = the perpendicular height of the cone.

Vol A = $pi times 14^2 times 35/3 = 7183.77 cm^3$

Vol B = $pi times 7^2 times 25/3 = 1282.82 cm^3$

Therefore, Vol B would fit into cup A.
How high will cup A be filled?

$pir^2h/3 = V$

$h/3 = V/(pir^2)$

$h = 3(V/(pir^2))$

$h = 3(1282.82/(pi times 14^2))$

$= 6.25 cm$

Cups A and B are cone shaped and have heights of 35 cm35 cm and 23 cm23 cm and openings with radii of 14 cm14 cm and 7 cm7 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?