Question

Срочно,ПОЖАЛУЙСТА!!!! высота правильной четырехугольной призмы 8 см а ее объем 200см3 найти полную поверхность призмы

Answer 1

В основании правильной четырехугольной призмы находится квадрат.
a^2 × 8 = 200
a^2=25
a=5 (см)
Sполн=5^2 × 2 + 5 × 8 × 4= 50+160=210 (см^2)

Answer 2

Calculation of Prism Height

To find the height of a regular quadrilateral prism, we need to use the formula for the volume of a prism. The formula for the volume of a prism is given by:

Volume = Base Area x Height

In this case, we are given that the volume of the prism is 200 cm³ and the base area is not provided. Therefore, we need to find the base area first.

Calculation of Base Area

Since the prism is a regular quadrilateral prism, we can assume that the base is a square. Let's denote the side length of the square base as 's'. The area of a square is given by:

Area = s²

To find the side length of the square base, we can rearrange the formula for the volume of the prism:

Volume = Base Area x Height

Substituting the values we have:

200 cm³ = s² x Height

Now, we need to find the value of 's' using the given information.

Calculation of Side Length

Unfortunately, the side length of the square base is not provided in the given information. Therefore, we cannot calculate the exact value of the height of the prism.

However, we can still provide a general formula to calculate the height of the prism in terms of the side length of the square base. Let's denote the side length of the square base as 's' and the height of the prism as 'h'. The formula for the height of a regular quadrilateral prism in terms of the side length of the square base is given by:

Height = Volume / (s²)

Using this formula, you can substitute the given volume (200 cm³) and calculate the height of the prism when the side length of the square base is known.

Calculation of Total Surface Area

To find the total surface area of the prism, we need to consider the area of all the faces. A regular quadrilateral prism has two identical square bases and four rectangular faces.

The formula for the total surface area of a regular quadrilateral prism is given by:

Total Surface Area = 2 x Base Area + 4 x Lateral Area

Since we don't have the exact value of the base area and height, we cannot calculate the total surface area of the prism.

In summary, without the side length of the square base, we cannot calculate the exact height or total surface area of the prism.