Question

Найдите площадь полной поверхности тела полученного при вращении прямоугольного треугольника с катетами 3 см и 4 см вокруг большего катета

Answer 1

Решение дано на фото.

Answer 2

Calculation of the Surface Area of the Rotated Triangle

To find the surface area of the solid obtained by rotating a right-angled triangle with legs measuring 3 cm and 4 cm around the longer leg, we can use the formula for the lateral surface area of a cone.

The lateral surface area of a cone is given by the formula: A = πrℓ, where A is the surface area, r is the radius of the base, and ℓ is the slant height.

In this case, the longer leg of the right-angled triangle acts as the base of the cone, and the hypotenuse acts as the slant height. Therefore, the radius of the base is half the length of the longer leg, which is 2 cm.

To find the slant height, we can use the Pythagorean theorem. The slant height is equal to the square root of the sum of the squares of the two legs. In this case, it is equal to √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm.

Now we can substitute the values into the formula for the lateral surface area of a cone:

A = π(2 cm)(5 cm) = 10π cm^2.

Therefore, the surface area of the solid obtained by rotating the right-angled triangle with legs measuring 3 cm and 4 cm around the longer leg is 10π cm^2.