Finding volume by using cross section?

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Homework Help Overview

The original poster presents a problem involving finding the volume of a shape with a circular cross section, given that the area of the cross section is 1 m². The context suggests a focus on geometric properties related to volume calculation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the cross-sectional area and the radius of the circular shape. There are attempts to derive formulas for volume based on the shape being a cylinder or a sphere, while also questioning the necessary dimensions for volume calculation.

Discussion Status

Some participants have provided guidance on how to find the radius from the area and the formulas for volume based on different shapes. There is an exploration of how the length of the rod affects the volume, with examples given for different lengths. Multiple interpretations of the problem are being considered, but no consensus has been reached.

Contextual Notes

The discussion includes assumptions about the shape being a rod with a uniform cross section and the need for additional dimensions (length or height) to calculate volume. The original poster expresses uncertainty about the mathematical concepts involved.

exibo177
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Homework Statement



The only given data is that the cross section is 1m^2, the shape is circular (like a cut wire/rod) and i have to find the volume.

Homework Equations



from what I've searched, i found the equation:
39789.nce010.gif

but i have no idea what to do with it, i still haven't learned it at school.
if you know any other way to do it, please tell me with explanations. thank you!


The Attempt at a Solution

 
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If you have the cross section of a cylinder, then you can find the radius
[itex]A=\pi r^2 => r=\sqrt{A/\pi}[/itex]
From the radius, you could find the volume if you were dealing with a sphere, or if you are dealing with a cylinder, you would need a length/height.
[itex]V_{cylinder} = \pi r^2 l <br /> \\<br /> V_{sphere} = 4/3 \pi r^3[/itex]
 
Encephalon said:
If you have the cross section of a cylinder, then you can find the radius
[itex]A=\pi r^2 => r=\sqrt{A/\pi}[/itex]
From the radius, you could find the volume if you were dealing with a sphere, or if you are dealing with a cylinder, you would need a length/height.
[itex]V_{cylinder} = \pi r^2 l <br /> \\<br /> V_{sphere} = 4/3 \pi r^3[/itex]
So my A here is 1m^2?
 
To find the volume of a rod of uniform crossection area (square, circular, triangular...it does not matter) the equationis L x area
so if area is 1m^2 and the rod is 1 m long the volume is 1m^3, 10m long it is 10m^3 and so on
 
edit, misposted
please delete
 

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