# Calculations of a sphere

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?

Update:

• what are D1 and D2? Jun 9, 2022 at 0:40
• 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? Jun 9, 2022 at 1:33
• So draw it, either full size or to scale. Jun 9, 2022 at 4:02

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: 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 $$\pi/2$$ $$D_2=\pi\sqrt{r^2-(r-d_1)^2}$$
• 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 Jun 9, 2022 at 4:56