Question

Диагональ осевого сечения цилиндра образует с основанием угол ß. Найдите объем цилиндра, площадь боковой поверхности и площадь полной поверхности, если радиус основания равен k. Желательно с рисунком)

Answer 1

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Answer 2

Finding the Volume of a Cylinder

To find the volume of a cylinder, we need to know the radius of the base and the height of the cylinder. In this case, the radius of the base is given as k.

The formula for the volume of a cylinder is:

Volume = π * r^2 * h

Where: - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base - h is the height of the cylinder

Since the radius of the base is given as k, we can substitute it into the formula:

Volume = π * k^2 * h

Finding the Surface Area of the Lateral Surface

The lateral surface area of a cylinder is the sum of the areas of the two circular bases. The formula for the lateral surface area is:

Lateral Surface Area = 2 * π * r * h

Since the radius of the base is given as k, we can substitute it into the formula:

Lateral Surface Area = 2 * π * k * h

Finding the Total Surface Area of the Cylinder

The total surface area of a cylinder is the sum of the lateral surface area and the areas of the two circular bases. The formula for the total surface area is:

Total Surface Area = 2 * π * r * (r + h)

Since the radius of the base is given as k, we can substitute it into the formula:

Total Surface Area = 2 * π * k * (k + h)

Calculation Example

Let's assume the angle formed by the diagonal of the base with the base itself is ß. In this case, we are not given the height of the cylinder, so we cannot calculate the exact values for the volume, lateral surface area, and total surface area. However, we can provide the formulas and an example calculation using a hypothetical height value.

Let's say the height of the cylinder is h = 10. Using this value, we can calculate the volume, lateral surface area, and total surface area.

Volume = π * k^2 * h Volume = π * k^2 * 10

Lateral Surface Area = 2 * π * k * h Lateral Surface Area = 2 * π * k * 10

Total Surface Area = 2 * π * k * (k + h) Total Surface Area = 2 * π * k * (k + 10)

Please note that these calculations are based on the assumption of a given height value. If you have a specific value for the height, you can substitute it into the formulas to find the exact values for the volume, lateral surface area, and total surface area.

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