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A tapered shaft has a diameter of 5 centimeters at the small end and is 15 centimeters long. If the taper is 3°, find the diameter of the large end of the shaft.

DarkKnight  Jun 29, 2017
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Let's "slice" the shaft in half, cutting through the diameters of the ends, and look at this cross section.

 

Now we can see that the diameter of the large end   =   g + g + 5   =   2g + 5

 

And....

 

tan θ   =  opposite / adjacent

tan 3º  =  g / 15                              Multiply both sides of this equation by 15 .

15 tan 3º  =  g

 

So....

 

diameter of large end  =  2g + 5                    Substitute   15 tan 3º   in for   g  .

                                    =  2(15 tan 3º) + 5

                                    =  30 tan 3º  +  5        Put this into a calculator to get....

                                    ≈  6.572   cm

hectictar  Jun 29, 2017

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