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5 questions
12 votes
1 answer
4k views
Volume of the intersection of two cylinders
I have two infinite cylinders of unit radius in $\mathbb{R}^3$, whose axes are skew lines. Say that the axis of one is centered on the $x$-axis, and the axis of the other is determined by the two ...
- 31.2k
1 vote
1 answer
3k views
Volume of Intersection of cylinders (different radii)
I want to derive a formula for the area of the intersection of two rigth cylinders with different radii. To get an idea I attached a sketch. My idea is to determine the borders of $x$ and $z$ in ...
- 320
3 votes
4 answers
1k views
Calculating volume enclosed using triple integral
Calculate the volume enclosed between $x^2 + y^2=1$, $y^2+z^2=1$, $x^2+z^2=1$ I am supposed to solve this question using multiple integral. I am not able to visualize the resultant figure of whose I ...
user88923
10 votes
2 answers
3k views
Find volume of crossed cylinders without calculus.
I found this puzzle here. (It's labeled "crossed cylinders".) Here's the description: Two cylinders of equal radius are intersected at right angles as shown at left. Find the volume of ...
- 54.6k
31 votes
6 answers
24k views
Langley's Adventitious Angles
The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it. So ...
- 5,393