Question

Самостійна робота «ЦИЛІНДР» 1.Обчисліть: А) діагональ осьового переріза циліндра, Б) площу осьового S перерізу В) S основи Г) S біч. д)S повну якщо діаметр основи циліндра дорівнює 8 см, а твірна циліндра дорівнює 6 см. 2 . У циліндрі проведено, паралельно осі циліндра, площину, яка відтинає від кола дугу а. Січна площина перетинає основу по хорді, яка дорівнює b. Діагональ утвореного перерізу утворює кут 2B (B це бета) з твірною циліндра Знайдіть: а) радіус основи циліндра; б) площу основи циліндра; в) висоту циліндра; г) діагональ осьового перерізу; д) площу перерізу; БУДЬ ЛАСКА ПОВНЕ РОЗВ'ЯЗАННЯ З МАЛЮНКАМИ, ДАЮ 100 БАЛІВ!!!!

Answer 1

Calculation of Cylinder Parameters

To solve the given problem, we need to calculate various parameters of a cylinder. Let's break down the problem into smaller parts and solve them step by step.

# A) Diagonal of the Axis Cross-Section of the Cylinder

To calculate the diagonal of the axis cross-section of the cylinder, we need to use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the radius and the height of the cylinder.

Let's denote the radius of the cylinder as r and the height as h.

Using the Pythagorean theorem, the diagonal (d) can be calculated as:

d = √(r^2 + h^2)

# B) Area of the Axis Cross-Section (S)

The area of the axis cross-section of the cylinder can be calculated using the formula:

S = π * r^2

where π is a mathematical constant approximately equal to 3.14159.

# C) Area of the Base (S)

The area of the base of the cylinder can be calculated using the formula:

S = π * r^2

# D) Lateral Surface Area (S)

The lateral surface area of the cylinder can be calculated using the formula:

S = 2 * π * r * h

# Given Values

Let's denote the given values as follows: - Diameter of the base of the cylinder = 8 cm - Radius of the base of the cylinder = 8 cm / 2 = 4 cm - Height of the cylinder = 6 cm - Angle formed by the diagonal of the cross-section = 2B

# Solution

Now, let's solve the given problem step by step.

1. Calculation of Parameters: - A) Diagonal of the Axis Cross-Section of the Cylinder: - Given: Radius (r) = 4 cm, Height (h) = 6 cm - Using the formula: d = √(r^2 + h^2) - Substituting the values: d = √(4^2 + 6^2) - Calculating: d ≈ 7.211 cm [[1]].

- B) Area of the Axis Cross-Section (S): - Given: Radius (r) = 4 cm - Using the formula: S = π * r^2 - Substituting the value: S = π * 4^2 - Calculating: S ≈ 50.265 cm^2 [[2]].

- C) Area of the Base (S): - Given: Radius (r) = 4 cm - Using the formula: S = π * r^2 - Substituting the value: S = π * 4^2 - Calculating: S ≈ 50.265 cm^2 [[2]].

- D) Lateral Surface Area (S): - Given: Radius (r) = 4 cm, Height (h) = 6 cm - Using the formula: S = 2 * π * r * h - Substituting the values: S = 2 * π * 4 * 6 - Calculating: S ≈ 150.796 cm^2 [[3]].

2. Calculation of Additional Parameters: - a) Radius of the Base of the Cylinder: - Given: Diameter of the base = 8 cm - Radius (r) = Diameter / 2 = 8 cm / 2 = 4 cm

- b) Area of the Base of the Cylinder: - Given: Radius (r) = 4 cm - Using the formula: S = π * r^2 - Substituting the value: S = π * 4^2 - Calculating: S ≈ 50.265 cm^2 [[2]].

- c) Height of the Cylinder: - Given: Height (h) = 6 cm

- d) Diagonal of the Axis Cross-Section of the Cylinder: - Given: Angle formed by the diagonal = 2B - The diagonal forms a right triangle with the radius and height of the cylinder. - The angle formed by the diagonal is 2 times the angle formed by the radius and height. - The angle formed by the radius and height is denoted as B (beta). - Therefore, the angle formed by the diagonal is 2B. - To find the diagonal, we need the value of B.

3. Solution for Additional Parameters: - a) Radius of the Base of the Cylinder: 4 cm - b) Area of the Base of the Cylinder: ≈ 50.265 cm^2 [[2]] - c) Height of the Cylinder: 6 cm - d) Diagonal of the Axis Cross-Section of the Cylinder: To be determined

Please provide the value of 'b' (the chord length) and the angle 'B' (beta) to proceed with the calculation of the remaining parameters.