The height of the cylinder is 16 cm. At a distance of 6 cm from the axis of the cylinder a section

| September 26, 2021 | education

The height of the cylinder is 16 cm. At a distance of 6 cm from the axis of the cylinder a section is drawn parallel to the axis of the cylinder and having the shape of a square. Find the radius of the cylinder

Since, according to the condition, the section ABB1A1 is axial, and there is a square in the section, the sides of the section are equal to the height of the cylinder. OO1 = AA1 = BB1 = AB = A1B1 = 16 cm.

Consider a triangle O1A1B1, in which OA1 and OB1 are equal to each other as the radii of the circle. Then the triangle O1A1B1 is equilateral. Let’s draw the height О1Н, which will also be the median, since the triangle is equilateral, then А1Н = В1Н = А1В1 / 2 = 16/2 = 8 cm.

In a right-angled triangle О1НА1, according to the Pythagorean theorem, we determine the length of the hypotenuse О1А1.

O1A1 ^ 2 = O1H ^ 2 + A1H ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100.

О1А1 = 10 cm.

Answer: The radius of the circle at the base of the cylinder is 10 cm.



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