The height of the straight cylinder is 8m, the radius of the base is 5m.

| September 4, 2021 | education

The height of the straight cylinder is 8m, the radius of the base is 5m. The cylinder is crossed by a plane parallel to its axis. The cross section is a square. Find the distance from this section to the axis of the cylinder.

Let a cylinder be given with the axis OO1, the section ABCD is parallel to OO1, ABCD is a square, the height of the cylinder is 8 m, the radius of the base is 5 m.

Since ABCD is parallel to the axis, AB is equal to the height of the cylinder. AB = 8 m.Since ABCD is a square, then AD = 8 m.

Let’s draw the distance OH to the section. OH will be perpendicular to AD and intersect AD in the middle.

So AH = 8: 2 = 4 m.

OA is the radius of the base, OA = 5 m.

In the triangle AHO (angle H = 90 °), we find OH according to the Pythagorean theorem:

OH = √ (AO² – AH²) = √ (25 – 16) = √9 = 3 m.

Answer: the distance from the axis of the cylinder to the section is 3 m.



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