Not Your Usual Cylinder - Volume

If you take a rectangle and displace one of its sides parallel to the other side the area of the shape does not change. All the parallelograms thus formed have the same base length, the same perpendicular height and therefore have the same area. This is a 2-dimensional example of Cavalieri's principle .

Similarly, if you take a right cylinder and displace one of its flat faces parallel to the other flat face, then you obtain an oblique cylinder with the same volume as the original right cylinder. This is a 3-dimensional example of Cavalieri's principle .

The right cylinder will have the same perpendicular height as the oblique cylinder, $h = 4$ . The radius of the circular base will be $r =2$ . Therefore the volume of the right cylinder, and also the volume of the oblique cylinder is $\pi \times r^{2} \times h = \pi \times 2^{2} \times 4 = 16 \pi \approx \boxed{ 50.265}$ $_\square$

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You can also check out this interactive Math Open Reference link where you can adjust the height, radius, and the slant height of the cylinder and observe how the volume changes. (Click 'options' in lower right corner to 'allow oblique' and 'freeze height'.)

as per the given figure volume of oblique cylinder is equal to $π×r^2×l$ $sin \theta$ where $sin \theta$ is the angle formed between $l$ & $r$

so volume is equal to $π×4×5×\frac{4}{5}$ which comes up to be $\boxed {50.265}$ .