Question

Высота правильной четырехугольной пирамиды равна 20 см и образует с боковым ребром угол 45 градусов .найти объем пирамиды

Answer 1

Решение Вашего задания во вложении

Answer 2

В основании квадрат. Если высота с боковым  образует угол 45гр, то в прямоугольном треугольнике катеты равны,один яляется высотой, а другой половиной диагонали квадрата.Диагональ равна 2 высотам,т,е, 40см.Сторона будет равна 40/√2=20√2
V=1/3*(20√2)²*20=1600/3см³

Answer 3

Calculating the Volume of a Regular Quadrilateral Pyramid

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

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

Where: - Base Area is the area of the base of the pyramid - Height is the perpendicular height from the base to the apex of the pyramid

Given Information

- Height (h) = 20 cm - Angle between the height and a lateral edge = 45 degrees

Calculating the Base Area

The base of a regular quadrilateral pyramid is a square. To find the area of the base, we can use the formula for the area of a square:

Base Area = side^2

However, we need to find the length of the side of the base. To do this, we can use trigonometric functions.

Finding the Side Length of the Base

Given that the angle between the height and a lateral edge is 45 degrees, we can use trigonometric functions to find the side length of the base.

Using the trigonometric relationship: tan(45 degrees) = opposite/adjacent

We can solve for the side length of the base.

Calculating the Volume

Once we have the base area and the height, we can use the formula mentioned earlier to calculate the volume of the pyramid.

Let's proceed with these calculations.