Question

Основанием пирамиды служит прямоугольный треугольник с катетами 6 и 8 см. Боковые ребра наклонены к плоскости основания под углом 60(градусов). Найти объем пирамиды.

Answer 1

Решение в приложении.

Answer 2

Calculation of the Pyramid's Volume

To find the volume of the pyramid, we need to know the dimensions of the base and the height. In this case, the base of the pyramid is a right-angled triangle with legs measuring 6 cm and 8 cm. The lateral edges of the pyramid are inclined to the base plane at an angle of 60 degrees.

To calculate the volume of the pyramid, we can use the formula:

Volume = (1/3) * Base Area * Height

The base area can be calculated using the formula for the area of a right-angled triangle:

Base Area = (1/2) * Base * Height

In this case, the base of the pyramid is the right-angled triangle with legs measuring 6 cm and 8 cm. The height of the triangle can be found using the Pythagorean theorem:

Height = sqrt(6^2 + 8^2)

Now, let's calculate the volume of the pyramid.

Step 1: Calculate the height of the right-angled triangle (base of the pyramid) using the Pythagorean theorem:

Height = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 cm

Step 2: Calculate the base area of the pyramid using the formula for the area of a right-angled triangle:

Base Area = (1/2) * 6 cm * 8 cm = 24 cm^2

Step 3: Calculate the volume of the pyramid using the formula:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * 24 cm^2 * 10 cm = 80 cm^3

Therefore, the volume of the pyramid is 80 cm^3.

Please let me know if there's anything else I can help you with!