Question

Диагональ осевого сечения цилиндра 22,5 дм и образует с плоскостью основания угол 30 найти площадь сечения и площадь основания цилиндра

Answer 1

В осевом сечении рассмотрим треугольник с катетами Н и 2R и гипотенузой d
H=1/2d (против угла 30) = 11,25
2R=d·cos30=22,5·√3/2=11,25·√3
S сеч =2R·H=2025/16·√3
Sосн=πR²=π·45√3/8

Answer 2

Calculation of the Diagonal of the Cross-Section of a Cylinder

To find the diagonal of the cross-section of a cylinder, we need to know the diameter of the cross-section and the angle it forms with the plane of the base.

Given: - Diameter of the cross-section of the cylinder: 22.5 dm - Angle formed with the plane of the base: 30 degrees

To calculate the diagonal of the cross-section, we can use the formula:

Diagonal = Diameter / cos(Angle)

Substituting the given values into the formula, we have:

Diagonal = 22.5 dm / cos(30 degrees)

Now, let's calculate the diagonal using this formula.

Using the trigonometric identity cos(30 degrees) = sqrt(3)/2, we can simplify the calculation:

Diagonal = 22.5 dm / (sqrt(3)/2)

Simplifying further, we get:

Diagonal = 22.5 dm * (2 / sqrt(3))

Calculating the value, we find:

Diagonal ≈ 25.98 dm

Therefore, the diagonal of the cross-section of the cylinder is approximately 25.98 dm.

Calculation of the Area of the Cross-Section and Base of the Cylinder

To find the area of the cross-section and the base of the cylinder, we need to know the radius of the cross-section.

Given: - Diameter of the cross-section of the cylinder: 22.5 dm

To calculate the area of the cross-section and the base, we can use the formula:

Area = π * Radius^2

To find the radius, we divide the diameter by 2:

Radius = Diameter / 2

Substituting the given value into the formula, we have:

Radius = 22.5 dm / 2

Calculating the value, we find:

Radius = 11.25 dm

Now, let's calculate the area of the cross-section and the base using this formula.

Using the value of the radius, we have:

Area = π * (11.25 dm)^2

Calculating the value, we find:

Area ≈ 397.94 dm^2

Therefore, the area of the cross-section and the base of the cylinder is approximately 397.94 square dm.