Question

Диагональ осевого сечения цилиндра 17 см, а его высота 15 см. Найдите площадь поверхности цилиндра. Прошу помочь!

Answer 1

Ответ:

ответ на скрине.Решала в заметках

Answer 2

Finding the Surface Area of a Cylinder

To find the surface area of a cylinder, we need to calculate the sum of the areas of its two circular bases and the lateral surface area.

Given: - Diameter of the cylinder's axial section (which is equal to the diameter of the circular bases) = 17 cm - Height of the cylinder = 15 cm

To calculate the surface area of the cylinder, we'll follow these steps:

1. Calculate the radius of the circular bases: - The diameter of the axial section is given as 17 cm. - The radius is half the diameter, so the radius of the circular bases is 17 cm / 2 = 8.5 cm.

2. Calculate the area of each circular base: - The formula for the area of a circle is A = πr², where A is the area and r is the radius. - Substituting the radius value, we get A = π(8.5 cm)². - Calculating this, we find that the area of each circular base is approximately 226.98 cm².

3. Calculate the lateral surface area: - The lateral surface area of a cylinder is given by the formula A = 2πrh, where A is the lateral surface area, r is the radius, and h is the height. - Substituting the values, we get A = 2π(8.5 cm)(15 cm). - Calculating this, we find that the lateral surface area is approximately 2019.27 cm².

4. Calculate the total surface area: - The total surface area of a cylinder is the sum of the areas of the two circular bases and the lateral surface area. - Adding the areas of the circular bases (2 * 226.98 cm²) and the lateral surface area (2019.27 cm²), we get the total surface area of the cylinder. - Calculating this, we find that the total surface area of the cylinder is approximately 2473.23 cm².

Therefore, the surface area of the given cylinder with a diagonal of the axial section measuring 17 cm and a height of 15 cm is approximately 2473.23 cm².

Please let me know if there's anything else I can help you with!