Common Volume of 2 unequal cylinders with axis that don't intersect

[bigbsonnier]

1. This isn't homework, this is personal study, but i think it really fits the form of a "textbook style question".

I need to find the volume of two intersecting circular cylinders of unequal radius and axis that don't intersect but are at right angles.



2. i have no relevant equations assided from the common axis equations. i tried to look at the problem from a stand point of two circle segements and i think i blew a fuse in my head.

for those interested the common axis equation is located here

http://nistdigitalarchives.contentd...object/collection/p13011coll6/id/78660/rec/20

and here

https://www.physicsforums.com/showthread.php?t=18954





3. As stated before my attempt at a theoretical solution fried something so i will get the data i need right now empirically via 3d software but i know the answer to this question would help me in the future.

Thank you

 

[mighty2000]

for sharing your question with us. Finding the volume of intersecting cylinders may seem daunting, but with the right approach, it can be solved. Let's break down the problem into smaller parts and work towards a solution together.

First, let's define the variables we will be using. Let R1 and R2 be the radii of the two cylinders, and let L1 and L2 be their respective lengths. We can also define the distance between the centers of the cylinders as d.

To find the volume of the intersecting cylinders, we need to calculate the volume of each cylinder separately, and then subtract the overlapping volume. To do this, we can use the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height.

Let's start by finding the volume of the first cylinder, V1 = πR1²L1. Similarly, the volume of the second cylinder is V2 = πR2²L2.

Next, we need to find the overlapping volume. This can be done by finding the volume of the intersection of the two cylinders, which is essentially a cylinder with a height of d and a radius equal to the difference between the radii of the two cylinders, (R2 - R1). Using the formula for the volume of a cylinder, we get Voverlap = π(R2 - R1)²d.

Therefore, the total volume of the intersecting cylinders is Vtotal = V1 + V2 - Voverlap.

To calculate this volume, we need to know the values of R1, R2, L1, L2, and d. If you have access to 3D software, you can input these values and get the result. However, if you want to solve it theoretically, you will need to find a way to calculate these values.

One approach could be to use the Pythagorean theorem to find the length of the diagonal of the intersecting cylinders, which would give us the distance d. From there, we can use the axis equations you mentioned in your post to find the lengths L1 and L2.

I hope this helps you in your personal study. Good luck!