Constructing a Cubical Box to Within 3 cm3

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In summary, the problem is asking for the precision of the edge of a cubical box that can hold 125 cm3 within a margin of error of 3 cm3. The solution involves using the differential formula for volume and solving for the variation in the edge length that will result in a volume between 128 cm3 and 122 cm3. This is an approximate solution.
  • #1
synergix
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Homework Statement


a) A cubical box is to be built so that it holds 125 cm3. How precisely should the edge be made so
that the volume will be corrected to within 3 cm3?

The Attempt at a Solution



I am not sure even what this is asking exactly could someone decode if they have seen a similar problem before?
 
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  • #2
Yeah, it's just a differential problem, I think. V=a^3, so dV=3*a^2*da. If a=5cm then V=125cm^3. You are given dV=3cm^3. Solve for da. It's an approximate solution for how large the variation in a can be and still give you a V between 128cm^3 and 122cm^3. Approximate, mind you.
 
  • #3
I thought that the question might be asking something like that but it seemed kind of strange to me. thanks
 

FAQ: Constructing a Cubical Box to Within 3 cm3

How do I ensure that the box is within 3 cm3 of the desired volume?

The most accurate way to construct a cubical box within 3 cm3 is to use precise measuring tools, such as a ruler or caliper, and carefully follow the instructions for constructing a perfect cube. This may involve cutting and assembling the box from a larger piece of material.

What materials should I use to construct the box?

The choice of materials depends on the desired properties of the box. For a lightweight and inexpensive option, cardboard or foam board can be used. For a more durable and sturdy box, wood or plastic may be better options. Make sure to choose materials that can be easily cut and shaped to the desired size.

Is it necessary to use exact measurements for each side of the box?

Yes, it is important to use precise measurements for each side of the box in order to achieve a volume within 3 cm3 of the desired amount. Even a slight difference in measurement can significantly affect the final volume of the box.

Can I use any method to construct the box?

There are several different methods for constructing a cubical box, but some may be more accurate than others. It is important to carefully follow a method that ensures all sides are equal in length and the box is assembled correctly to achieve the desired volume.

How can I check the accuracy of the constructed box?

To check the accuracy of the constructed box, you can use a measuring tool to confirm that all sides are equal in length and that the volume is within 3 cm3 of the desired amount. You can also fill the box with water and measure the volume of water it holds to determine its accuracy.

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