Question

Цилиндр получен вращением прямоугольника со стороной 5 м и диагональю 13 м вокруг данной стороны. найдите площадь полной поверхности цилиндра.

Answer 1

дан прямоугольник наибольшая сторона 5м диагональ 13 

получается прямоугольный теуголник с гипотенузой 13и катет 5

нужно найти второй катет он и является радиусов окружности

по теореме пифагора

R^2=13^2 - 5^2=144

R=12

тепрь ищем площадь по формуле пи*R^2

S=3.14*144=452.16

ответ:452,16

Answer 2

Calculation of the Cylinder's Surface Area

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

1. Area of the Circular Bases: - The circular bases of the cylinder are formed by the rotation of the rectangle's sides. - The diameter of the circular bases is equal to the length of the rectangle's diagonal, which is 13 m. - The radius of the circular bases is half the diameter, so the radius is 13 m / 2 = 6.5 m. - The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. - Therefore, the area of each circular base is A = π(6.5 m)^2.

2. Lateral Surface Area: - The lateral surface area of a cylinder is given by the formula A = 2πrh, where A is the area, π is a mathematical constant approximately equal to 3.14159, r is the radius of the circular base, and h is the height of the cylinder. - In this case, the height of the cylinder is equal to the length of the rectangle's side, which is 5 m. - Therefore, the lateral surface area is A = 2π(6.5 m)(5 m).

3. Total Surface Area: - The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral surface area. - Therefore, the total surface area of the cylinder is A = 2π(6.5 m)^2 + 2π(6.5 m)(5 m).

Let's calculate the surface area of the cylinder using the given values:

A = 2π(6.5 m)^2 + 2π(6.5 m)(5 m)

A = 2π(42.25 m^2) + 2π(32.5 m^2)

A = 84.5π m^2 + 65π m^2

A = 149.5π m^2

Therefore, the surface area of the cylinder is approximately 149.5π square meters.

Note: The exact value of π depends on the level of precision required for the calculation. In this case, we have used the approximate value of π as 3.14159.