Question

Квадрат со стороной 5см вращается вокруг одной из сторон. Найти полную поверхность полученной фигуры вращения

Answer 1

У нас получается цилиндр . находим площадь окружностей формула Pr^2 . но у нас 2-е окружности получается 2Pr^2 = 2*3.14*25=157 . находим периметр окружности = 2Pr заметим что без квадрата и сразу скажу что P это число пи равное 3.14 . подстовляем 2*3.14*5 =31.4  находим боковую поверхность цилиндра высота равна 5 умножаем на 31.4 = 157 . 157+157=314.

Answer 2

Calculating the Surface Area of a Rotated Square

To find the surface area of the figure obtained by rotating a square with a side length of 5 cm around one of its sides, we can use the formula for the surface area of a solid of revolution. The surface area of the figure obtained by rotating a curve around the x-axis from x=a to x=b is given by the formula:

Surface Area = 2π∫[a, b] f(x) √(1 + (f'(x))^2) dx

Where f(x) is the function describing the curve being rotated. In this case, the function describing the square is a constant, so f(x) = 5.

Applying the Formula

Using the formula, we can calculate the surface area of the figure obtained by rotating the square.

Surface Area = 2π∫[0, 5] 5 √(1 + 0) dx

Simplifying, we get:

Surface Area = 10π∫[0, 5] 5 dx

Integrating, we get:

Surface Area = 10π * 5x | [0, 5]

Substituting the limits of integration, we get:

Surface Area = 50π * (5 - 0)

Surface Area = 250π

Conclusion

Therefore, the surface area of the figure obtained by rotating a square with a side length of 5 cm around one of its sides is 250π square centimeters.