Maximum dimensions-very interesting

In summary, the conversation revolved around designing a container box with maximum volume by cutting out the four corners of a square cardboard sheet. The dimensions of the box were determined to be a square base with a height of 20/3 cm and a side length of 80/3 cm. The process involved finding a value for "a" that would result in a maximum volume, which was found to be 20/3. The conversation also briefly touched on the use of latex in mathematical equations.
  • #1
joejo
150
0
maximum dimensions-very interesting!

hey guys...i have another question...i posted my answer right below it...does it look right guys?! I hope so! Thanks in advance

You are to design a container box by cutting out the four corners of a square cardboard sheet that is 1600cm^2 in area. The box must have a square base and an open top. Determine the dimensions of the box that give maximum value.

The side of the square cardboard is 40 cm. Let side of corner square is a cm. The volume of the box V = (40-2a)2.a cm3 , For max volume we have dV/da = 0 implies (20-3a)(20-a) = 0, i.e., a = 20, a = 20/3. But when a = 20, V = 0. So to maximize the volume a = 20/3. So the base of is a square of side 80/3 cm and height = 20/3 cm.

Sorry not good with latex...
 
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  • #2
Yes, that looks good. It's intuitively clear that a=20/3 should be a maximum (there must be 'some' maximum between a=0 and a=20), but for completeness you might want to show it is a maximum indeed (depends on your teacher).
 
  • #3
thanks for your help!
 

Related to Maximum dimensions-very interesting

1. What are maximum dimensions and why are they important in science?

Maximum dimensions refer to the largest size or extent that something can attain. In science, this concept is important because it helps us understand the limitations and boundaries of the physical world and the laws that govern it.

2. How do scientists determine the maximum dimensions of an object or system?

Scientists use various methods such as mathematical calculations, experiments, and observations to determine the maximum dimensions of an object or system. They also take into account factors such as physical laws, materials, and environmental conditions.

3. Can the maximum dimensions of an object or system change over time?

Yes, the maximum dimensions of an object or system can change over time. This can be due to factors such as growth, decay, or external influences. It is important for scientists to constantly study and update their understanding of maximum dimensions as new information and discoveries are made.

4. Are there different types of maximum dimensions in science?

Yes, there are different types of maximum dimensions in science. For example, there is the maximum size or volume that an object can attain, the maximum speed that an object can travel, and the maximum amount of energy that can be produced by a system. Each type of maximum dimension is governed by different physical laws and principles.

5. How do maximum dimensions relate to the concept of infinity?

Maximum dimensions and infinity are closely related concepts, but they are not the same. Maximum dimensions refer to a specific size or limit, while infinity represents something that has no limits or boundaries. In some cases, maximum dimensions can approach infinity, but they can never truly reach it. Scientists use both concepts to understand and study the physical world.

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