A section is drawn in the cylinder with a plane parallel to the axis of the cylinder. The distance from the axis

| September 18, 2021 | education

A section is drawn in the cylinder with a plane parallel to the axis of the cylinder. The distance from the axis of the cylinder to the section is 8 cm. The radius of the cylinder is 17 cm. Find the diagonal of the section of the cylinder if it is known that the given section is a square.

The AOB triangle is equilateral, since OA = OB = R = 17 cm. The OH height in the AOB triangle is also the median, then AH = BH = AB / 2.

In the right-angled triangle AOН, we determine the length of the leg AH using the Pythagorean theorem.

AH ^ 2 = OA ^ 2 – OH ^ 2 = 289 – 64 = 225.

AH = 15 cm.

Then AB = AH * 2 = 30 cm.

Since, by condition, the section ABCD is square, then AD = AB = 30 cm.

In a right-angled triangle ABD, we find the length of the diagonal BD.

BD ^ 2 = AB ^ 2 * AD ^ 2 = 30 ^ 2 + 30 ^ 2 = 900 * 900 = 1800.

ВD = 30 * √2 cm.

Answer: The diagonal of the section is 30 * √2 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.