The height of the cylinder is 8 dm, the radius of the base is 5 dm. The cylinder is cut by a plane parallel

| September 2, 2021 | education

The height of the cylinder is 8 dm, the radius of the base is 5 dm. The cylinder is cut by a plane parallel to the axis of the cylinder so that a square is formed in the section. Find the distance of this section from the axis.

Since the section АА1В1В has the shape of a square, then АА1 = А1В1 = BB1 = AB = 8 dm.

From the center O1 of the circle, draw the radii O1A1 and O1B1.

Since O1A1 = O1B1 = R = 5 dm, the triangle O1A1B1 is isosceles. The height O1H in an isosceles triangle is also the median of the triangle, which means it divides the base of A1B1 in half. HA1 = HB1. Then HA1 = HB1 = A1B1 / 2 = 8/2 = 4 cm.

In a right-angled triangle HO1A1, we determine the length of the leg O1H using the Pythagorean theorem.

O1H ^ 2 = O1A1 ^ 2 – HA1 ^ 2 = 25 – 16 = 9.

О1Н = 3 dm.

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



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