Formula of a truncated cone

[mermaidly]

Hey guys!
Could somebody help me figure out how the following formula for the
variation of the section with x is obtained?
I don't understand where comes 2-x/L and why is it squared?
Thanks in advance.

 

[Dr.Peterson]

Could somebody help me figure out how the following formula for the
variation of the section with x is obtained?
I don't understand where comes 2-x/L and why is it squared?
Thanks in advance.

View attachment 26694

View attachment 26693

The radius is a linear function of x. What is that function? (Think of a line through two given points, or else use similar triangles.)

Then you'll be squaring the radius to find the cross-sectional area.

 

[lex]

Draw a picture of the part you are interested in. Mark in what you are looking for and what you know.



You'll then see that you can find the length [MATH]y_1[/MATH], using similar triangles.
Then write down the length [MATH]y_2[/MATH] and that is the radius of the circular cross-section of the cone, which you are interested in.
You can write down the area and it should become what you are looking for.