Is the equation "0 <= x <= 3, 0<= y <= 4, 0 <= z <= 5" for a cuboid?

  • Thread starter Nat3
  • Start date
In summary, the given problem involves sketching a volume and finding its area. The notation used includes three inequalities representing the boundaries of the volume. The region is bounded by 6 planes and can be visualized as a rectangular solid or cuboid.
  • #1
Nat3
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Homework Statement


Sketch the following volume and find the area.


Homework Equations


0 <= x <= 3, 0<= y <= 4, 0 <= z <= 5


The Attempt at a Solution


The notation is confusing me. Is the equation simply representing a cuboid?
 
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  • #2
If that's all the info you are given, yes.
 
  • #3
That's not "an equation", it's three different inequalities. The first, [itex]0\le x\le 3[/itex] means all points (x, y, z) such that the component, x, is between 0 and 3. That region is bounded by the two planes x= 0 and x= 3.
Similarly [itex]0\le y\le 4[/itex] defines a region bounded by the planes y= 0 and y= 4. Finally, [itex]0\le z\le 5[/itex] defines the region bounded by the planes z= 0 and z= 5. Those 6 planes form the 6 sides of a rectangular solid or cuboid.
 

What is a cuboid?

A cuboid is a three-dimensional shape with six rectangular faces and eight vertices. It is also known as a rectangular prism.

What does the equation "0 <= x <= 3, 0<= y <= 4, 0 <= z <= 5" represent?

This equation represents the dimensions of a cuboid, with x representing the length, y representing the width, and z representing the height. It states that the length must be between 0 and 3 units, the width between 0 and 4 units, and the height between 0 and 5 units.

How is this equation used to calculate the volume of a cuboid?

The equation is used to calculate the volume of a cuboid by multiplying the length, width, and height together. In this case, the volume would be 3 x 4 x 5 = 60 cubic units.

Can the dimensions of a cuboid be greater than the values specified in the equation?

Yes, the dimensions of a cuboid can be greater than the values specified in the equation. The equation only sets limits on the possible dimensions, but a cuboid can have any dimensions within those limits.

Is this equation applicable to all cuboids?

No, this equation is only applicable to cuboids with a specific range of dimensions. Cuboids with different dimensions may require a different equation to represent their dimensions.

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