Cilla H.

asked • 01/08/16

HELP HUGE MATH PROJECT

For my math project I have to choose which shape for an ice cube would be best to design- a cube, a sphere or a cylinder. Things I also have to do are:
- Find and simplify the volume-to-surface-area ratio for each of the three possible ice shapes.
-  Use the ratios to choose the best shape and what may be the best size for that shaped ice cube. 
I then have to consider the following questions:
- Since the purpose of ice is to keep drinks cold, is it better for the ice cube to have a high volume or a low volume? 
- Is it better for an ice cube to have a larger surgace area of a smaller purpose area? 
- Which volume-to-surface-area ratio would be better for an ice cube, the lowest possible or highest possible?
- How does increasing the of an objecf affect its volume-to-surface-area ratio? 
And finaly I have to create a visual model displaying my ice cube design, including the dimensions, volume and surface area of my ice. I really honestly dont even know where to start. This is a simple project but I really struggle with stuff like this. Please help explain how to do these things and what I am doing exactly. If any tutor is willing to help me I will be extremely grateful!!! Thank you so much! 
 

Hilton T.

tutor
You should contact a tutor to work 1 to 1 with you on projects. An assignment of this scope cannot be discussed effectively on this forum.
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01/08/16

Bijan M.

Heat transfer is proportional to area, so the most efficient ice would have the largest surface area to volume ratio. If you have ice shaped like sphere, cube, cylinder, each with similar proportions, then the cube would have the largest surface to volume ratio. Sphere has the smallest. That's why when you are cold you get goose bumps. The bumps on your skin are semi-spheres, so they reduce your skin's surface area, which helps your body conserve heat. So lets say a cube with each side length R, volume would be R^3, surface area would be 6R^2. Surface to volume ratio would be 6R^2/R^3 = 6/R. Cylinder area would be 2piR^2 + 2piR*R (making height also R). volume would be piR^2*R = piR^3. surface to volume ratio would be 2piR^2/piR^3 + 2piR^2/piR^3 = 2/R + 2/R = 4/R Sphere surface area is 4piR^3. Volume is 4/3piR^3. surface to volume ratio is 4piR^2 / 4/3piR^3 = 3/R
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01/30/20

1 Expert Answer

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Robin G. answered • 03/21/20

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I can see how this project can be daunting. I would be happy to help, but I would like to see the Rubric for the project first. I do agree - hiring an online tutor for a few sessions would be helpful to you!


Are you looking for longer cooling time or a quick lowering of temperature?


Your key is to start with the surface area to volume ratio. This means to calculate the surface area of each 3-D form and compare it in a ratio to the volume of each form.


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