Question

Найдите площадь боковой поверхности тела, полученного при вращении прямоугольного треугольника с катетами 4 см и 7 см, вокруг большого катета(с рисунком)

Answer 1

Меньший катет является радиусом основания конуса,
больший - высотой конуса.
Площадь боковой поверхности конуса:
                   S = πRL, где L - образующая.
По т. Пифагора:
                   L = √(R²+h²) = √(16+49) = √65 ≈ 8,06 (см)
Тогда:
                   S = πRL = 12,56√65 ≈ 12,56*8,06 = 101,26 (см²)

Ответ: ≈ 101,26 см²

Answer 2

Calculation of the lateral surface area of the rotated triangle

To find the lateral surface area of the body obtained by rotating a right-angled triangle with legs of 4 cm and 7 cm around the larger leg, we need to calculate the circumference of the circle formed by the rotation.

The larger leg of the triangle, which is the base of the rotated body, has a length of 7 cm.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.

To find the radius, we need to divide the length of the base (7 cm) by 2, since the base of the triangle is the diameter of the circle.

Therefore, the radius r is equal to 7 cm / 2 = 3.5 cm.

Now we can calculate the circumference C using the formula:

C = 2πr = 2π * 3.5 cm = 7π cm.

The lateral surface area of the body is equal to the circumference of the circle, which is 7π cm.

Answer:

The lateral surface area of the body obtained by rotating a right-angled triangle with legs of 4 cm and 7 cm around the larger leg is 7π cm.