+0  
 
+1
516
1
avatar+422 

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
 #1
avatar+7324 
+2

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

10 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.