Calculate Volume of Bowling Pin Using Simpson's Rule

  • Thread starter okevino
  • Start date
Just remember to use the measurements of the circumference as the y values and follow the steps for Simpson's rule to approximate the volume. In summary, the conversation involves finding the volume of revolution of a bowling pin with a length of 36cm using Simpson's rule. The measurements of the circumference every 4cm are provided and should be used as y values in the calculations. The formula for volume of revolution is also mentioned as well as the need to square the y values to use Simpson's rule.
  • #1
okevino
13
0
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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  • #2
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.
 
  • #3
what do i do with the [tex]y^2[/tex]
 
  • #4
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.
 
  • #5
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..
 
  • #6
No problem.
 

FAQ: Calculate Volume of Bowling Pin Using Simpson's Rule

How do you use Simpson's Rule to calculate the volume of a bowling pin?

Simpson's Rule is a numerical integration technique used to approximate the area under a curve. In order to use Simpson's Rule to calculate the volume of a bowling pin, you will need to have a function that represents the shape of the pin and a set of discrete data points that approximate the curve of the pin. You can then use Simpson's Rule formula to calculate the volume by summing up the products of the function values at each data point and the corresponding weight factors.

What is the formula for Simpson's Rule?

The formula for Simpson's Rule is V ≈ (h/3) * (y0 + 4y1 + 2y2 + 4y3 + ... + 4yn-1 + yn), where h is the interval between each data point and yi is the function value at the ith data point.

How accurate is Simpson's Rule for calculating the volume of a bowling pin?

The accuracy of Simpson's Rule depends on the number of data points used and the smoothness of the curve being approximated. Generally, the more data points used, the more accurate the approximation will be. However, Simpson's Rule is known to be more accurate than other numerical integration techniques, such as the Trapezoidal Rule, for functions that are relatively smooth.

Can Simpson's Rule be used to calculate the volume of any shape?

Simpson's Rule can be used to calculate the volume of any shape as long as the shape can be represented by a function and a set of discrete data points can be obtained to approximate the curve of the shape. However, it may not be the most efficient or accurate method for all shapes.

Are there any limitations to using Simpson's Rule for calculating the volume of a bowling pin?

One limitation of using Simpson's Rule for calculating the volume of a bowling pin is that it assumes the shape of the pin can be represented by a single function. If the pin has multiple curves or irregularities, it may be difficult to find a single function that accurately represents the shape. In this case, other methods such as numerical integration using computer software may be more suitable.

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