Question

Осевым сечением цилиндра является квадрат диагональ которого 8 см, найдите обьем цилиндра

Answer 1

$V = \pi * R^{2} *h$
Осевое сечение - квадрат ( по условию) , его диагональ = 8 см,
=> а√2 = 8 , сторона квадрата  а= 4√2 (см)
высота = а = 4√2 (по усл сечение -  квадрат)
радиус = а/2 => R=2√2 (cм)
подставляем в формулу, получаем:
V= π * 2√2 * 2√2 * 4√2 = 32√2  *π (куб см)

Answer 2

Finding the Volume of a Cylinder

To find the volume of a cylinder, we need to know the radius of the base and the height of the cylinder. However, in this case, we are given the diagonal of the base square, which is 8 cm.

To find the radius of the base, we can use the relationship between the diagonal and the side length of a square. In a square, the diagonal is equal to the side length multiplied by the square root of 2. Therefore, the side length of the square base is 8 cm divided by the square root of 2.

Let's calculate the side length of the square base first:

Side length of the square base:

The diagonal of the square base is 8 cm. The side length of the square base is the diagonal divided by the square root of 2.

Using this information, we can calculate the side length of the square base:

Side length = diagonal / √2 = 8 cm / √2 = 8 cm / 1.414 ≈ 5.657 cm.

Now that we have the side length of the square base, we can find the radius of the cylinder.

Radius of the cylinder:

The radius of the cylinder is half the side length of the square base.

Radius = side length / 2 = 5.657 cm / 2 = 2.8285 cm.

Now we have the radius of the cylinder, but we still need the height to calculate the volume.

Unfortunately, the height of the cylinder is not provided in the question. Without the height, we cannot calculate the volume of the cylinder.

Please provide the height of the cylinder so that we can calculate the volume for you.