Question

Диагональ осевого сечения цилиндра равна 10 см и образует угол 30° с образующей цилиндра. Найти длину окружности основания цилиндра.

Answer 1

Там 30 гр.,где не видно.

Answer 2

Calculation of the Length of the Base Circumference of the Cylinder

To find the length of the base circumference of the cylinder, we need to use the given information about the diagonal of the cross-section and the angle it forms with the axis of the cylinder.

Let's break down the problem step by step:

1. The diagonal of the cross-section of the cylinder is given as 10 cm. 2. The diagonal forms an angle of 30° with the axis of the cylinder.

To find the length of the base circumference, we can use trigonometry. Let's denote the radius of the cylinder as r and the height of the cylinder as h.

From the given information, we can form a right triangle with the diagonal of the cross-section as the hypotenuse, the radius of the cylinder as one of the legs, and the height of the cylinder as the other leg.

Using trigonometric functions, we can relate the angle, the radius, and the height of the cylinder as follows:

sin(30°) = r / 10 Simplifying the equation, we get:

r = 10 * sin(30°) = 5 cm

Now that we have the radius of the cylinder, we can calculate the length of the base circumference using the formula:

C = 2 * π * r

Substituting the value of r into the formula, we get:

C = 2 * π * 5 = 10π cm

Therefore, the length of the base circumference of the cylinder is 10π cm.

Please let me know if I can help you with anything else.