Question

Площадь осевого сечения = S , угол между диагональю сечения и плоскостью основания = α.Найти объем цилиндра

Answer 1

Площадь диагонального сечения равна произведению диаметра основания D  на высоту цилиндра H.
Так как диагональ осевого сечения- гипотенуза прямоугольного треугольника с катетами D и H
и острым углом α, то H=D·tgα
S=D·H    ⇒    S= D·D·tgα      ⇒ $D= \sqrt{ \frac{S}{tg \alpha } }$
V=S(осн)·H= πR²H=$\pi \frac{D ^{2} }{4}Dtg \alpha = \frac{S \sqrt{S} }{4 \sqrt{tg \alpha } }$

Answer 2

Finding the Volume of a Cylinder

To find 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 the area of the cross-section and the angle between the diagonal of the cross-section and the plane of the base.

Let's denote the area of the cross-section as S and the angle between the diagonal of the cross-section and the plane of the base as α.

To find the volume of the cylinder, we can use the formula:

V = S * h

where V is the volume, S is the area of the base, and h is the height of the cylinder.

However, we don't have the height of the cylinder given in the question. Without the height, we cannot calculate the volume of the cylinder.

If you have any additional information or if there is anything else I can assist you with, please let me know!