The section of a cylinder by a plane parallel to its axis is a square that cuts off an arc of 90

| September 23, 2021 | education

The section of a cylinder by a plane parallel to its axis is a square that cuts off an arc of 90 degrees from the base circle. Find the height of the cylinder if the distance from the axis of the cylinder to this section is 5 cm

In a flat drawing, consider a part of the base of the cylinder – a circle from which a 90 ° arc is cut off.

OA = OB – circle radii, ∠AOB = 90 °.

OH = 5 cm by condition as the distance from the axis of the cylinder to the secant plane, and at the same time it is the height and bisector of the isosceles right-angled triangle AOB.

Triangles AOH and BOH are also rectangular and isosceles.

OH = AH = AB = 5 cm.

AB = 5 * 2 = 10 cm.

The second side of the square (the height of the cylinder) is also 10 cm.

Answer: the height of the cylinder is 10 cm.



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