Understanding Inner and Outer Radius

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In summary, the conversation is about understanding the concept of finding the mass of a material needed to make a hollow spherical shell with inner radius r1 and outer radius r2. The concept involves finding the volume of the shell by subtracting the volume of a sphere of radius r1 from the volume of a sphere of radius r2, and then using the density to calculate the mass or vice-versa. The difference between the two radii represents the thickness of the shell.
  • #1
mysticxhobo
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Im new to these forums and I'm looking forward to becoming a regular contributor. I'm attempting to prepare for physics in the fall and I have a textbook problem that i understand the process of solving but not understand the concept.

Heres the question:
What mass of a material w/ density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2?

I understand everything besides the inner and outer radius part. What is the textbook trying to say with that statement. How do you know to subtract them? So if you understood to subtract the radii can you please explain your thought process?

Again thanks a alot.
 
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  • #2
'Hollow' means 'It ain't dere no mo.'

If I have a 'hollow spherical shell', it means the outer surface of the sphere has a radius 'r2' for instance and the inside surface of the hollow spherical shell, which isn't there, has a radius of 'r1' for instance.
 
  • #3
The difference between the two radii is the thickness of the shell. You can determine the volume of the shell by subtracting the volume of a sphere of radius r1 from the volume of a sphere of radius r2. Once you know the volume of the shell, you can calculate its mass with a given density or vice-versa.
 

FAQ: Understanding Inner and Outer Radius

1. What is the difference between inner and outer radius?

The inner radius refers to the distance from the center of a circle or sphere to its inner edge, while the outer radius refers to the distance from the center to its outer edge. Essentially, the inner radius is the radius of the hole or empty space within the circle or sphere, while the outer radius is the radius of the entire shape.

2. How do you measure inner and outer radius?

The inner and outer radius can be measured using a ruler or measuring tape. For a circle, simply measure the distance from the center to the edge. For a sphere, measure the distance from the center to the surface. Alternatively, you can use a compass to draw a circle or sphere and measure the distance between the center and the edge.

3. What is the importance of understanding inner and outer radius?

Understanding inner and outer radius is important in many fields, including mathematics, engineering, and science. It allows us to accurately calculate the area, volume, and circumference of circles and spheres, and is crucial in designing and building structures such as bridges, wheels, and pipes.

4. Can the inner radius be larger than the outer radius?

No, the inner radius cannot be larger than the outer radius. The inner radius is always smaller than or equal to the outer radius, as it represents the distance from the center to a point on the edge of the shape. If the inner radius were larger than the outer radius, it would mean that the shape is reversed or inside out.

5. How does the inner and outer radius affect the strength of a structure?

The inner and outer radius play a significant role in the strength of a structure. In general, the greater the difference between the inner and outer radius, the stronger the structure will be. This is because a larger difference between the two radii creates a thicker and more stable shape, allowing it to withstand greater forces and weight without collapsing or bending.

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