Question

Длина прямоугольного параллелепипеда 15 сантиметров она больше ширины в 3 раза а высота больше ширины на 3 сантиметра Найдите сумму длин всех ребер, и площадь его поверхность, обьем

Answer 1

1) ширина: 15:3 = 5 см

2) высота: 5+3 = 8 см

3) сумма ребер: 4*15  +  4*5  +  4*8 = 60 + 20 + 32 = 112 см

4) площадь поверхности: 2(15*5) + 2(15*8) + 2(5*8) = 150 + 240 + 80 = 470 см^2

5) объем: 15*5*8 = 600 см^3.

Ответ: 112 см;  470 см^2;  600 см^3.

Answer 2

Calculation of Dimensions

To find the sum of the lengths of all edges, the surface area, and the volume of the rectangular parallelepiped, we need to determine its dimensions based on the given information.

Let's assign variables to the dimensions of the rectangular parallelepiped: - Length: L - Width: W - Height: H

According to the given information: - The length is 15 centimeters. - The length is 3 times greater than the width. - The height is 3 centimeters greater than the width.

Based on these relationships, we can set up the following equations:

1. L = 15 cm 2. L = 3W 3. H = W + 3 cm

Solving for the Dimensions

To find the values of L, W, and H, we can substitute the given information into the equations and solve them simultaneously.

From equation 2, we can substitute L = 3W into equation 1: 3W = 15 cm

Solving for W: W = 15 cm / 3 W = 5 cm

Substituting W = 5 cm into equation 3: H = 5 cm + 3 cm H = 8 cm

Therefore, the dimensions of the rectangular parallelepiped are: - Length (L) = 15 cm - Width (W) = 5 cm - Height (H) = 8 cm

Calculation of Sum of Edge Lengths

To find the sum of the lengths of all edges, we can use the formula: Sum of Edge Lengths = 4L + 4W + 4H

Substituting the values we found: Sum of Edge Lengths = 4(15 cm) + 4(5 cm) + 4(8 cm) Sum of Edge Lengths = 60 cm + 20 cm + 32 cm Sum of Edge Lengths = 112 cm

Therefore, the sum of the lengths of all edges of the rectangular parallelepiped is 112 centimeters.

Calculation of Surface Area

To find the surface area of the rectangular parallelepiped, we can use the formula: Surface Area = 2(LW + LH + WH)

Substituting the values we found: Surface Area = 2(15 cm * 5 cm + 15 cm * 8 cm + 5 cm * 8 cm) Surface Area = 2(75 cm² + 120 cm² + 40 cm²) Surface Area = 2(235 cm²) Surface Area = 470 cm²

Therefore, the surface area of the rectangular parallelepiped is 470 square centimeters.

Calculation of Volume

To find the volume of the rectangular parallelepiped, we can use the formula: Volume = Length * Width * Height

Substituting the values we found: Volume = 15 cm * 5 cm * 8 cm Volume = 600 cm³

Therefore, the volume of the rectangular parallelepiped is 600 cubic centimeters.

In summary: - The sum of the lengths of all edges is 112 centimeters. - The surface area is 470 square centimeters. - The volume is 600 cubic centimeters.