Question

Срочно!!Диагональ осевого сечения цилиндра=12 см и образует с плоскостью нижней основы угол 45. Найти объем цилиндра.

Answer 1

Извиняюсь за неаккуратность, но вроде решается так

Answer 2

Calculation of the Cylinder's Volume

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 cross-section of the cylinder and the angle it forms with the plane of the base. We can use this information to find the radius and height of the cylinder.

Let's denote the diagonal of the cross-section as d and the angle it forms with the plane of the base as θ.

To find the radius (r) and height (h), we can use the following formulas:

r = (d / 2) * sin(θ).

h = (d / 2) * cos(θ).

Once we have the radius and height, we can calculate the volume of the cylinder using the formula:

Volume = π * r^2 * h.

Let's substitute the given values into the formulas to find the radius and height:

d = 12 cm (given).

θ = 45° (given).

r = (12 / 2) * sin(45°) = 6 * 0.7071 ≈ 4.2426 cm.

h = (12 / 2) * cos(45°) = 6 * 0.7071 ≈ 4.2426 cm.

Now, we can calculate the volume of the cylinder:

Volume = π * (4.2426)^2 * 4.2426 ≈ 226.195 cm^3.

Therefore, the volume of the cylinder is approximately 226.195 cm^3.

Please note that the above calculations assume that the cross-section of the cylinder is circular. If the cross-section is not circular, the calculations would be different.

I hope this helps! Let me know if you have any further questions.