Question

Высота цилиндра равна 16 см на расстояНии 6 см от оси цилиндра проведено сечение параллельное оси цилиндра и имеющая форму квадрата. найти радиус цилиндра

Answer 1

Если сечение имеет форму квадрата, то хорда сечения равна высоте, т.е. 16 см. И по теореме Пифагора находим радиус. R =√(6²+8²)=10. 8 см - это половина хорды, а 6 см - расстояние от хорды до центра.

Answer 2

Finding the Radius of the Cylinder

To find the radius of the cylinder, we need to use the information given about the height and the distance from the axis of the cylinder to the square-shaped section.

Let's break down the problem step by step:

1. The height of the cylinder is given as 16 cm. 2. The distance from the axis of the cylinder to the square-shaped section is given as 6 cm.

To find the radius, we can use the Pythagorean theorem. The distance from the axis to the square-shaped section forms a right triangle with the radius of the cylinder as the hypotenuse.

Let's denote the radius of the cylinder as R.

Using the Pythagorean theorem, we can write the equation:

R^2 = (Height of the cylinder)^2 - (Distance from the axis to the square-shaped section)^2

Substituting the given values:

R^2 = 16^2 - 6^2

Simplifying the equation:

R^2 = 256 - 36

R^2 = 220

Taking the square root of both sides:

R = √220

Calculating the square root of 220, we find that the radius of the cylinder is approximately 14.832 cm.

Therefore, the radius of the cylinder is approximately 14.832 cm.