Question

Прямоугольный параллелепипед и куб имеют равные площади поверхности.Длина параллелепипеда равна 18м, что в 2 раза больше. чем его ширина. и на 8м больше. чем его высота.Найдите ребро куба

Answer 1

Длинна параллелепипеда - 18 м, ширина - 18 : 2 = 9 м, высота - 18 - 8 = 10.

S(бок) = 2*(a*b + b*c +a*c) = 2*(18*9 + 9*10 + 18*10) = 864 (м)

S(бок) у куба = 6a^2

а = ${ \sqrt{864:6} }$ = ${ \sqrt{144} }$ = 12.

Answer 2

Finding the Edge Length of the Cube

To find the edge length of the cube, we can use the information given about the rectangular parallelepiped. Let's break down the information provided:

- The length of the rectangular parallelepiped is 18 meters, which is twice the width. - The length is also 8 meters more than the height.

Let's assign variables to the width, height, and length of the rectangular parallelepiped:

- Let w be the width. - Let h be the height. - Let l be the length.

From the given information, we can write the following equations:

1. The length is twice the width: l = 2w. 2. The length is 8 meters more than the height: l = h + 8.

To find the edge length of the cube, we need to find a relationship between the dimensions of the rectangular parallelepiped and the cube. Since the rectangular parallelepiped and the cube have equal surface areas, we can equate their surface areas.

The surface area of a rectangular parallelepiped is given by the formula:

Surface Area = 2lw + 2lh + 2wh

The surface area of a cube is given by the formula:

Surface Area = 6s^2, where s is the edge length of the cube.

Equating the surface areas of the rectangular parallelepiped and the cube, we have:

2lw + 2lh + 2wh = 6s^2

Substituting the values of l and w from the given information, we get:

2(2w)w + 2(2w)h + 2wh = 6s^2

Simplifying the equation, we have:

4w^2 + 4wh + 2wh = 6s^2

4w^2 + 6wh = 6s^2

Now, let's substitute the value of l from equation 2:

4w^2 + 6wh = 6(h + 8)^2

Simplifying further, we have:

4w^2 + 6wh = 6(h^2 + 16h + 64)

4w^2 + 6wh = 6h^2 + 96h + 384

Since we have two variables, w and h, we need another equation to solve for them. Unfortunately, the given information does not provide another equation. Therefore, we cannot determine the exact values of w and h.

However, we can still find the relationship between the edge length of the cube (s) and the dimensions of the rectangular parallelepiped (w and h). Let's assume a value for w and solve for h:

Let's assume w = 1.

Substituting w = 1 into the equation, we have:

4(1)^2 + 6(1)h = 6h^2 + 96h + 384

Simplifying, we get:

4 + 6h = 6h^2 + 96h + 384

6h^2 + 90h + 380 = 0

Solving this quadratic equation, we find that h ≈ -1.26 or h ≈ -10.

Since the height cannot be negative, we discard the solution h ≈ -1.26.

Therefore, we have h ≈ -10.

Now, let's substitute **