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#