Question

Обьем правильной 6-угольной пирамиды 6см Сторона основания 1 см найти боковое ребро

Answer 1

Обьем пирамиды равен треть площади основания умножить на высоту;
V=1/3 * S*h
S=(3*sqrt(3)*a*a)/2; a=1 => S=2,6
h - то есть боковое ребро = v/1/3s = 6/0,86=7

Answer 2

Calculating the Volume of a Regular Hexagonal Pyramid

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

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

Given: - Side length of the base (s) = 1 cm - Height of the pyramid (h) = 6 cm

Calculating the Area of the Base

The area of a regular hexagon can be calculated using the formula:

Area = (3 * √3 * s^2) / 2

Substitute the value of the side length (s = 1 cm) into the formula to find the area of the base.

Area = (3 * √3 * 1^2) / 2

Area = (3 * √3) / 2

Calculating the Volume

Now, we can use the area of the base and the height to find the volume of the pyramid.

Volume = (1/3) * (3 * √3) / 2 * 6

Volume = √3 * 6

Volume = 6√3 cm³

Finding the Length of the Lateral Edge

The lateral edge (l) of a regular hexagonal pyramid can be calculated using the formula:

l = √(h^2 + (s/2)^2)

Substitute the values of the height (h = 6 cm) and the side length of the base (s = 1 cm) into the formula to find the length of the lateral edge.

l = √(6^2 + (1/2)^2)

l = √(36 + 1/4)

l = √(144/4 + 1/4)

l = √(145/4)

l = √145 / 2

So, the length of the lateral edge of the regular hexagonal pyramid is √145 / 2 cm.