I apologize if the question is very basic, I admit I'm not the best at math and physics.

I am doing an experiment with a sphere, the measurements are as follows:

  • The sphere has a diameter of 330 mm (13 inches)
  • D1 measures 75mm

I want D2 to be attached to D1 and both ends of D2 to be attached to the sphere. D1 must be attached to one end of the sphere. I want to know how long D2 should be. How can I do that calculation?

enter image description here

Update: enter image description here

enter image description here

  • $\begingroup$ what are D1 and D2? $\endgroup$
    – jsotola
    Commented Jun 9, 2022 at 0:40
  • $\begingroup$ I know that a sphere has no end, obviously, but I am referring to one of the extremes, I don't know if I make myself understood. D2 is a tube that will be attached to the sphere "up" and "down", D1 is a box that measures 75mm. I want to know how long the tube (D2) should measure. D1 and D2 will go together. I want everything to be glued, that is, D1 is glued to one of the ends of the sphere and to D2... and D2 is glued to the sphere. How big should the D2 be? $\endgroup$ Commented Jun 9, 2022 at 1:33
  • $\begingroup$ So draw it, either full size or to scale. $\endgroup$
    – Solar Mike
    Commented Jun 9, 2022 at 4:02

1 Answer 1


First, consider a circle with same diameter as the sphere, with the distance $d_2$ being the projection of $D_2$ onto the plane and assuming $d_1=D_1$ relative to your figure:enter image description here The radius of the circle is equal to the radius of the sphere, i.e. $r=165$mm.
We get a planar measure for $d_2$ that is $$d_2=2\sqrt{r^2-(r-d_1)^2}$$ To get the length $D_2$ in 3D, we multiply $d_2$ by $\pi/2$ $$D_2=\pi\sqrt{r^2-(r-d_1)^2}$$

  • $\begingroup$ If you can explain it to me better, I will thank you from the bottom of my heart. If you help me with the answer I will also appreciate it, so I can practice with other numbers to see if I understood correctly. (Many thanks for your explanation) $\endgroup$ Commented Jun 9, 2022 at 4:23
  • $\begingroup$ What is unclear ? $\endgroup$
    – drC1Ron
    Commented Jun 9, 2022 at 4:26
  • $\begingroup$ I get 434.46 mm $\endgroup$
    – drC1Ron
    Commented Jun 9, 2022 at 4:35
  • $\begingroup$ sqrt(165^2-(165-75)^2) = 138.29 What am I doing wrong? web2.0calc.es (copy and paste the formula that I placed sqrt..., so you can verify it quickly) $\endgroup$ Commented Jun 9, 2022 at 4:46
  • $\begingroup$ Please realize that the distance $d_2$ is not the same as $D_2$. My figure is in 2D but a sphere is in 3D. Multiply 138.29 by $\pi$ to get the same answer as me $\endgroup$
    – drC1Ron
    Commented Jun 9, 2022 at 4:56

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