Question

В цилиндре через середину радиуса основания проведено сечение перпендикулярно радиусу. Сечение образует квадрат площадью 16 см 2 . Вычислите объем цилиндра.

Answer 1

Ответ:

на фото решение

Объяснение:

Answer 2

Calculation of the Cylinder Volume

To calculate the volume of a cylinder, we need to know the area of the base and the height of the cylinder. In this case, we are given that the section formed by cutting through the middle of the base perpendicular to the radius is a square with an area of 16 cm^2.

Let's denote the side length of the square as s. Since the square is formed by cutting through the middle of the base, the side length of the square is equal to the diameter of the base, which is twice the radius. Therefore, s = 2r.

The area of the square is given as 16 cm^2, so we have the equation:

s^2 = 16

Substituting s = 2r, we can rewrite the equation as:

(2r)^2 = 16

Simplifying, we get:

4r^2 = 16

Dividing both sides by 4, we have:

r^2 = 4

Taking the square root of both sides, we find:

r = 2

Now that we know the radius of the base, we can calculate the volume of the cylinder. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height of the cylinder.

Since the section formed by cutting through the middle of the base is perpendicular to the radius, it divides the height of the cylinder into two equal parts. Therefore, the height of the cylinder is twice the side length of the square, which is 2s.

Substituting s = 2r, we have:

h = 2(2r) = 4r = 4(2) = 8

Now we can calculate the volume of the cylinder:

V = π(2^2)(8) = 4π(8) = 32π

Therefore, the volume of the cylinder is 32π cubic units.

Please note that the value of π is approximately 3.14159.