Question

Сторона основания правильной шестиугольной призмы равна 2 см а высота 5 см.Найдите полную поверхность и объём призмы

Answer 1

Calculation of the Surface Area and Volume of a Prism

To find the surface area and volume of a prism, we need to know the length of the base and the height of the prism. In this case, the length of the base of the prism is given as 2 cm, and the height is given as 5 cm.

Surface Area of a Prism

The surface area of a prism is the sum of the areas of all its faces. For a right hexagonal prism like the one described, the surface area can be calculated using the formula:

Surface Area = 6 * (Area of the Base) + (Perimeter of the Base) * (Height)

Since the base of the prism is a regular hexagon, we can calculate the area of the base using the formula:

Area of the Base = (3 * sqrt(3) * (Side Length)^2) / 2

In this case, the side length of the base is given as 2 cm. Let's substitute the values into the formulas to find the surface area.

Area of the Base = (3 * sqrt(3) * (2 cm)^2) / 2 = 6 * sqrt(3) cm^2

Perimeter of the Base = 6 * (Side Length) = 6 * 2 cm = 12 cm

Surface Area = 6 * (6 * sqrt(3) cm^2) + (12 cm) * (5 cm) = 72 * sqrt(3) cm^2 + 60 cm^2

Therefore, the full surface area of the prism is 72 * sqrt(3) cm^2 + 60 cm^2.

Volume of a Prism

The volume of a prism can be calculated using the formula:

Volume = (Area of the Base) * (Height)

Substituting the values into the formula, we get:

Volume = (6 * sqrt(3) cm^2) * (5 cm) = 30 * sqrt(3) cm^3

Therefore, the volume of the prism is 30 * sqrt(3) cm^3.

Please note that the calculations provided are based on the given dimensions and formulas.