Need to find the volume of a rounded cube.

In summary, the conversation discusses the calculation of the volume of a cube with rounded corners. The cube has a volume of 8 cubic meters and the rounded corners have a length of 406mm. The suggested formula for finding the volume is width * height * depth, but the person is unsure how to proceed. Another person suggests thinking of the rounded corners as part of a sphere and using the difference between the volume of the sphere and the volume of the cube to find the volume of the rounded corners. The person asking for help confirms that this process is correct and shares their calculated answer of 7.755 square meters.
  • #1
alf_garnett
5
0
Hello everyone. I'm currently working on a project (independent study and not homework) and I find myself having to calculate the volume of a cube with rounded corners and I'm stumped. Any help would be really appreciated.

The cube itself is 8 cubic meters (2m on each side) and the rounded corners are 406mm from what would otherwise be a corner point to the end of the curve in all three directions spreading out from the would-be corner point. I need to be fairly precise with this calculation but I'm afraid my mathematics know-how isn't getting me very far. I appreciate the fact that this a learning forum and so I do not expect a direct answer to this but if somebody would be good enough to provide me with a formula into which I can put these figures I would really be very grateful. I've included an image of my problem in case I'm not being very well understood. Thank you all for reading.

1. Find the volume of a cube with rounded corners
Volume of un-rounded cube 2³ = 8 cubic meters.
Length of rounding = 406mm

2. Width * Height * Depth ... after that I just dunno.



3. Completely Stumped.
 

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  • #2
Is the curve describing your rounded corner a circle?
 
  • #3
It is, yes. Sorry, I should have mentioned that.
 
  • #4
If you took all 8 rounded corners of the cube and put them together you would have a sphere of radius 406 mm wouldn't you? And that sphere plus the part that was shaved off would be a little cube, right? So you can figure out how much was shaved off...
 
  • #5
Ahhhh - how simple it all seems when it's spelled out :D lol - I feel so thick. Thank you very very much LCKurtz. I really appreciate that. I do believe I can work this out now. I'll get back and post my result soon. Thank you.
 
  • #6
So I came up with the answer 7.755 square meters (rounded off). I calculated the volume of the sphere of radius 406mm, subtracted that from the volume of a 812mm cube and then subtracted the result of that from my 8 square meters to get the answer above. 7.754941. I have to ask ... did I follow the right process?
 
  • #7
alf_garnett said:
So I came up with the answer 7.755 square meters (rounded off). I calculated the volume of the sphere of radius 406mm, subtracted that from the volume of a 812mm cube and then subtracted the result of that from my 8 square meters to get the answer above. 7.754941. I have to ask ... did I follow the right process?

I didn't check your numbers but the process looks OK. Be sure about your units -- you have mm and m and volume is m3.
 

Related to Need to find the volume of a rounded cube.

1. What is a rounded cube?

A rounded cube is a three-dimensional shape with six equal square faces and rounded edges, similar to a regular cube but with curved edges instead of sharp corners.

2. How do you find the volume of a rounded cube?

To find the volume of a rounded cube, you can use the formula V = (4/3)πr³, where r is the radius of the curved edges. Alternatively, you can also find the volume by multiplying the length of one side by itself three times, as the sides of a rounded cube are all equal.

3. Can the volume of a rounded cube be measured in different units?

Yes, the volume of a rounded cube can be measured in different units as long as all the measurements are in the same unit. For example, if the length of one side is in inches, then the volume will be in cubic inches.

4. How do you measure the radius of a rounded cube?

You can measure the radius of a rounded cube by taking the distance from the center of one curved edge to the corner of the adjacent square face. Alternatively, if you know the length of one side of the cube, you can divide it by 2 to get the radius.

5. What are some real-life applications of finding the volume of a rounded cube?

Finding the volume of a rounded cube has many practical applications, such as in engineering and architecture for designing curved structures. It can also be used in manufacturing to determine the amount of material needed for curved objects. Additionally, it is essential in mathematics and physics for solving problems related to volume and surface area.

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