## Task 25/63

From a board, a circle with diameter $d=2 r$, a square with side $a=2 r$, and an isosceles triangle with base $a=2 r$ and height $b=2 r$ have been cut out.

Which body can be pushed through each of the three openings so that it completely fills them?
The solution is found when the body is represented in the three-plane projection (figure on the next page). It then turns out that one projection is a circle, the second projection is a square, and the third projection is an isosceles triangle.

Accordingly, it must be a cylinder with the height of the diameter, from which two symmetrical cylindrical segments are cut off along an axial section.

![](https://cdn.mathpix.com/cropped/2024_06_06_1d2be4837fb839c2b31dg-075.jpg?height=748&width=831&top_left_y=1890&top_left_x=612)