Calculate Volume of Bowling Pin Using Simpson's Rule

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around calculating the volume of a bowling pin using Simpson's Rule, focusing on the application of numerical integration techniques to a solid of revolution. Participants explore the necessary steps and mathematical concepts involved in the calculation.

Discussion Character

  • Mathematical reasoning, Homework-related, Technical explanation

Main Points Raised

  • One participant presents the dimensions of the bowling pin and provides circumference measurements at intervals, suggesting a method to approximate the volume using Simpson's Rule.
  • Another participant clarifies that the volume of revolution can be expressed as an integral involving the square of the function representing the circumference measurements.
  • A question is raised about how to handle the \(y^2\) term in the volume formula.
  • A response indicates that participants can calculate \(y^2\) from the given measurements and apply Simpson's Rule to this squared function.
  • One participant expresses uncertainty about the process but indicates progress in understanding the method after receiving assistance.

Areas of Agreement / Disagreement

Participants appear to agree on the general approach of using Simpson's Rule for volume approximation, but there is no consensus on the specific application details or the handling of the \(y^2\) term.

Contextual Notes

There are unresolved questions regarding the application of Simpson's Rule to the squared function and the integration process, as well as potential assumptions about the measurements and their accuracy.

okevino
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a bowling pin is 36cm long and is a solid of revolution.
the following are measurement of the circumference every 4cm.
from the top.

6.2 22 18.8 16.3 18.8 27 32.7 31.4 28.3

use simpson to appro the volum...


is this how to do this question?
(36/4)/3 [6.2 + 4(22) + 2(16.3) + ... + 28.3]
=1686.3
 
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This is the method you should do. Now the measurements along the circumference is y.

The volume of revolution between a and b, around the x-axis of a function y is given by

[tex]\pi \int^b_a y^2 dx[/tex]

So now use simpsons rule to approximate the integral, and multiply the result by pi.
 
what do i do with the [tex]y^2[/tex]
 
Well you know what y is, you can work out y^2.

You would know how to apply simpsons rule on y, try it on y^2.
 
cuz there's no answer to my questions..
so i just trying to learn how to do it...
thanks man.. i think i got it..
 
No problem.
 

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