George L.

asked • 05/31/22

Taylor wants to determine if the ice ring will float in the punch bowl with 9.3% of the ice ring extended above the surface of the punch.

Question Taylor wants to determine if the ice ring will float in the punch bowl with 9.3% of the ice ring extended above the surface of the punch. What will happen if Taylor puts the ice ring into the punch bowl? (will it overflow or not) 


desc: Taylor used a form to make an ice ring, a piece of ice shaped like a cylinder with a hole in the middle that is shaped like a cylinder.


Info

The volume of the ice ring is 375 cubic in3

distance from the top of the bowl is 14.98in

Stanton D.

Not enough info to solve. Need to know two more things: density of the punch, and dimensions of the bowl. You can't know the rise of the liquid (the mass of the ice displaces that mass of punch) unless you know what the free volume is to the top of the bowl. A linear dimension doesn't tell you that! Suggestion: dunk Taylor in the punch bowl instead, for giving you incomplete information.
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06/01/22

Wendy D.

tutor
Agree with Stanton. There's physics as well as geometry in this problem.
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06/09/22

Barry D.

tutor
The ice ring has a volume of V = 375. The volume of ice in bowl will be 0.907(375) from 100% - 9.3% outside = 90.7% = 0.907. V = 340.125. The ice ring will displace 340.125. The bowl as half a sphere holds a volume of 0.5(4/3)(pi*r^3) = 7040.35 with r = 14.98 The volume of punch must be less than or equal to 7040.35 - 340.125 = 6700.225 in^3 rounded to 6700 in^3 which it's approximately 29 gallons.
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06/12/22

Dean C.

tutor
There is not enough information to solve this problem. Barry's solution assumed that the radius of the bowl is 14.98 in. But, the problem states that the 14.98 in is the distance of the top of the liquid to the top of the punch bowl. Do not need to know the density of the punch. By knowing the volume of the ice submerged. It will displace an equal volume of liquid. But, we do need more information about the punch bowl. to determine how much volume is remaining in the last 14.98 in.
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06/13/22

Dean C.

tutor
It is not clear if the question is asking, will the ring float with 9.3 % exposed. Or if that is given. I suspect that it is given. If it is given then the density is not needed. The volume displace by the Ice ring will equal the volume of liquid displaced. If it is not given that the ice ring will have 9.3% of its volume exposed, then not only will we need the density of the punch (although we could probably assume the density of the punch is the density of water, since it is likely mostly water), but we will need more details about the ice ring to determine the percent that will be exposed. We would need outside diameter(or radius) and height of the cylinder and the diameter of the hole. Then we can calculate when the mass of the water displaced equals the mass of the ice ring. Also, a 30 gallon punch bowl is unlikely. The largest punch bowl I found on Amazon was a 3 gallon punch bowl.
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06/13/22

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