Question

ПЛИЗ ПОМОГИТЕ!! ЕСЛИ МОЖНО, ТО С РИСУНКАМИ ,БУДУ ОЧЕНЬ БЛАГОДАРНА 1)высота конуса равна 10 см , угол между высотой и образующей равен 45 градусов . найти площадь сечения 2) диагональ осевого сечения равностороннего цилиндра равна 8 см. Насти площадь основания цилиндра.

Answer 1

Task 1: Finding the Area of a Cone's Cross-Section

To find the area of a cross-section of a cone, we need to know the height of the cone and the angle between the height and the slant height (also known as the generatrix).

Given: - Height of the cone = 10 cm - Angle between the height and the generatrix = 45 degrees

To find the area of the cross-section, we can use the formula:

Area of cross-section = (1/2) * height * generatrix

In this case, the generatrix is the slant height of the cone, which can be found using the height and the angle between the height and the generatrix.

To find the generatrix, we can use trigonometry. The generatrix can be calculated using the formula:

generatrix = height / sin(angle)

Let's calculate the generatrix first:

generatrix = 10 cm / sin(45 degrees)

Using a calculator, we find that sin(45 degrees) is approximately 0.7071. Therefore:

generatrix ≈ 10 cm / 0.7071 ≈ 14.1421 cm

Now, we can calculate the area of the cross-section:

Area of cross-section = (1/2) * 10 cm * 14.1421 cm

Using a calculator, we find that:

Area of cross-section ≈ 70.7107 cm²

So, the area of the cross-section of the cone is approximately 70.7107 cm².

Task 2: Finding the Area of the Base of an Equilateral Cylinder

To find the area of the base of an equilateral cylinder, we need to know the diagonal of the axial section of the cylinder.

Given: - Diagonal of the axial section of the cylinder = 8 cm

To find the area of the base, we can use the formula:

Area of base = (4/√3) * (diagonal of axial section)²

Let's calculate the area of the base:

Area of base = (4/√3) * (8 cm)²

Using a calculator, we find that:

Area of base ≈ 138.5641 cm²

So, the area of the base of the cylinder is approximately 138.5641 cm².

I hope this helps! Let me know if you have any further questions.