Question

Осевое сечение цилиндра – квадрат, площадь которого равна 80 см. Найдите площадь сечения, проведенного параллельно оси цилиндра , если его диагональ равна 10 см.

Answer 1

Диаметр цилиндра является отдной стороной квадрата, высота цилиндра другой.

Находим их D=H=√80

В осевом сечении площадь которого требуется найти лежит прямоугольник. Одна сторона известра( высота цилиндра)=√80

Вторую сторону ищим по теореме пифагора 10^2-(√80)^2=√20

Находим площадь сечения √20*√80=√1600=40см^2

Answer 2

Answer in detail. The axial section of a cylinder is a square with an area of 80 cm. Find the area of the section parallel to the axis of the cylinder, if its diagonal is 10 cm.

To solve this problem, we need to use the properties of a cylinder and a square. A cylinder is a solid figure with two congruent circular bases that are parallel to each other. A square is a quadrilateral with four equal sides and four right angles. The diagonal of a square divides it into two congruent right triangles.

Let us denote the side of the square by a, the height of the cylinder by h, and the radius of the base by r. Then, we have the following relationships:

- The area of the square is equal to the square of its side: S = a^2 - The diagonal of the square is equal to the side times the square root of two: d = a√2 - The height of the cylinder is equal to the side of the square: h = a - The radius of the base is equal to half of the diagonal of the square: r = d/2 = a√2/2

Now, we can use the given information to find the values of a and r. We have:

- S = 80 cm^2 - d = 10 cm

Substituting these values into the formulas above, we get:

- a^2 = 80 - a√2 = 10

Solving for a, we get:

- a = √80 ≈ 8.94 cm - r = a√2/2 ≈ 6.32 cm

The area of the section parallel to the axis of the cylinder is equal to the area of the base, which is a circle. The area of a circle is equal to pi times the square of the radius. Therefore, the area of the section is:

- A = πr^2 ≈ 3.14 * 6.32^2 ≈ 125.28 cm^2

This is the final answer. The area of the section parallel to the axis of the cylinder is approximately 125.28 cm^2.