Question

Прямоугольный треугольник АВС вращают вокруг гипотенузы ВС = 10 см . Найдите объём полученного тела если m(∠ С )= 60 ° Помогите пожалуйста

Answer 1

Вот решение..............

Answer 2

Calculating the Volume of the Solid

To find the volume of the solid obtained by rotating the right-angled triangle ABC around its hypotenuse BC, we can use the formula for the volume of a cone. Since rotating a right-angled triangle around its hypotenuse forms a cone, we can use the formula:

Volume of cone = (1/3) * π * r^2 * h

Where: - r is the radius of the base of the cone - h is the height of the cone

Calculating the Radius and Height of the Cone

To find the radius and height of the cone, we can use the properties of the right-angled triangle and the given angle.

First, let's calculate the radius of the base of the cone. Since the hypotenuse BC is the diameter of the base of the cone, the radius r is half of BC.

r = BC / 2

Now, let's calculate the height of the cone. The height of the cone is the perpendicular from the vertex C of the triangle to the base of the cone. We can use trigonometric ratios to find the height.

Given that m(∠ C) = 60° and BC = 10 cm, we can use the trigonometric ratio for the sine of an angle in a right-angled triangle:

sin(60°) = opposite / hypotenuse

Calculating the Volume

Now that we have the radius and height of the cone, we can use the formula for the volume of a cone to calculate the volume of the solid obtained by rotating the triangle around its hypotenuse.

I'll calculate the radius and height and then use the formula to find the volume.