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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?

Answer 1

Ella Armstrong

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#

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Answer 2

Caroline Aucoin

Yes, cup A will overflow. When cup B, which is smaller, is completely emptied into cup A, it will fill cup A to its maximum capacity, causing cup A to overflow.

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