Question

Диагональ основания правильной четырехугольной пирамиды равна 8 см,а ее высота 12 см.найдите объем пирамиды

Answer 1

В основании лежит квадрат, т.к пирамида правильная. сторана квадрата будет равна 4*корень из 2. объем примиды тогда будет равен 128

Answer 2

Calculating the Volume of a Pyramid

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

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

In this case, the base of the pyramid is a square, so the area of the base can be calculated using the formula for the area of a square: Area of Base = (Side Length)^2.

Given: - Diagonal of the base of the pyramid = 8 cm - Height of the pyramid = 12 cm

Calculating the Side Length of the Base

To find the side length of the base of the pyramid, we can use the formula for the diagonal of a square: Diagonal = Side Length * √2.

From Source we can use the formula for the diagonal of a square to find the side length: d = a√2 where d is the diagonal and a is the side length.

Calculating the Area of the Base

Once we have the side length of the base, we can calculate the area of the base using the formula for the area of a square: Area of Base = (Side Length)^2

Calculating the Volume

Finally, we can use the formula for the volume of a pyramid to calculate the volume: Volume = (1/3) * (Area of Base) * Height

Let's calculate the side length of the base, the area of the base, and then the volume of the pyramid.