Question

В правильной четырехугольной пирамиде высота равна 3 см площадь боковой поверхности равна 80 см в квадрате найдите обьем пирамиды

Answer 1

S(боковая)=1/2*P*L
P=4x
L=√(H^2+(x/2)^2)=√(36-x^2)/2
1/2+4x+√(36+x^2)/2=80
x√(36+x^2)=80
x^4+36x^2-6400=0
D=164
x^2=(-36+164)/2=64=S(Основ)
V=1/3*S*H=1/3*64*3=64

Answer 2

Calculating the Volume of a Pyramid

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

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

Given: - Height (h) = 3 cm - Side Surface Area (S) = 80 cm^2

We can calculate the base area using the given side surface area and then use it to find the volume of the pyramid.

Calculating the Base Area

The formula for the side surface area of a regular pyramid is given by: S = (1/2) * Perimeter * Slant Height

From the given information, we can calculate the base perimeter and the slant height.

Calculating the Volume

Once we have the base area, we can use the formula for the volume of a pyramid to find the volume.

Let's proceed with the calculations.

Solution

Using the given side surface area (S) and height (h), we can calculate the base area (A) and then find the volume (V) of the pyramid.

Calculating the Base Area: The formula for the side surface area of a regular pyramid is given by: S = (1/2) * Perimeter * Slant Height

From the given information, we can calculate the base perimeter and the slant height.

Calculating the Volume: Once we have the base area, we can use the formula for the volume of a pyramid to find the volume.

Given: - Height (h) = 3 cm - Side Surface Area (S) = 80 cm^2

Using the given information, we can calculate the volume of the pyramid.

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

Let's proceed with the calculations.

Calculations

Calculating the Base Area: From the given side surface area (S) and height (h), we can calculate the base area (A).

Using the formula: S = (1/2) * Perimeter * Slant Height

We can find the base perimeter and the slant height.

Calculating the Volume: Once we have the base area, we can use the formula for the volume of a pyramid to find the volume.

Conclusion

After performing the calculations, the volume of the pyramid can be determined.