Question

В правильной четырёхугольной пирамиде высота равна 8 см, боковое ребро - 10 см. Найдите объём пирамиды.

Answer 1

Вот думаю все будет понятно

Answer 2

Calculation of the Volume of a Pyramid

To find the volume of a pyramid, we can use the formula:

Volume = (1/3) * base area * height

In this case, we are given that the height of the pyramid is 8 cm and the length of one of the lateral edges (which is also the base edge) is 10 cm.

To calculate the base area, we need to find the length of the base diagonal. We can use the Pythagorean theorem to do this.

Let's denote the base diagonal as d. We can find d using the formula:

d = sqrt((base edge/2)^2 + height^2)

Substituting the given values, we have:

d = sqrt((10/2)^2 + 8^2) = sqrt(25 + 64) = sqrt(89)

Now that we have the base diagonal, we can calculate the base area using the formula for the area of an isosceles triangle:

base area = (1/2) * base edge * base diagonal

Substituting the given values, we have:

base area = (1/2) * 10 * sqrt(89) = 5 * sqrt(89)

Finally, we can calculate the volume of the pyramid using the formula mentioned earlier:

Volume = (1/3) * base area * height

Substituting the values we have calculated, we get:

Volume = (1/3) * 5 * sqrt(89) * 8 = (40/3) * sqrt(89) cm^3

Therefore, the volume of the pyramid is (40/3) * sqrt(89) cm^3.

Please note that the answer is an approximation since the value of sqrt(89) is irrational.