Question

Прямоугольного параллелепипеда равны 36 см 25 см и 32 см Найдите сумму длин всех его ребер и площадь поверхности параллелепипеда

Answer 1

Площадь поверхности:
S = 2 * (ав + вс + ас),
S = 2 * (36*25 + 25*32 + 36*32) = 2 * (900 + 800 + 1152) = 2 * 2852= 5704 см²,

длина всех ребер:
L = 4 * (а + в + с),
L = 4 * (36 + 25 + 32) = 4 * 93 = 372 см

Answer 2

Calculation of the Sum of the Lengths of All Edges

To find the sum of the lengths of all edges of a rectangular parallelepiped, we need to add up the lengths of all twelve edges.

Given the dimensions of the rectangular parallelepiped as 36 cm, 25 cm, and 32 cm, we can calculate the sum of the lengths of all edges as follows:

1. The length of each edge is equal to the sum of the lengths of the three dimensions it connects. Therefore, the length of each edge can be calculated as follows:

- Edge 1: 36 cm + 25 cm + 32 cm = 93 cm - Edge 2: 36 cm + 25 cm + 32 cm = 93 cm - Edge 3: 36 cm + 25 cm + 32 cm = 93 cm - Edge 4: 36 cm + 25 cm + 32 cm = 93 cm - Edge 5: 36 cm + 25 cm + 32 cm = 93 cm - Edge 6: 36 cm + 25 cm + 32 cm = 93 cm - Edge 7: 36 cm + 25 cm + 32 cm = 93 cm - Edge 8: 36 cm + 25 cm + 32 cm = 93 cm - Edge 9: 36 cm + 25 cm + 32 cm = 93 cm - Edge 10: 36 cm + 25 cm + 32 cm = 93 cm - Edge 11: 36 cm + 25 cm + 32 cm = 93 cm - Edge 12: 36 cm + 25 cm + 32 cm = 93 cm

2. To find the sum of the lengths of all edges, we add up the lengths of all twelve edges:

- Sum of the lengths of all edges = 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm + 93 cm = 1116 cm

Therefore, the sum of the lengths of all edges of the rectangular parallelepiped is 1116 cm.

Calculation of the Surface Area of the Parallelepiped

To find the surface area of a rectangular parallelepiped, we need to calculate the areas of all six faces and then add them up.

Given the dimensions of the rectangular parallelepiped as 36 cm, 25 cm, and 32 cm, we can calculate the surface area as follows:

1. The surface area of each face can be calculated as the product of the lengths of two adjacent dimensions. Therefore, the surface area of each face can be calculated as follows:

- Face 1: 36 cm * 25 cm = 900 cm² - Face 2: 36 cm * 25 cm = 900 cm² - Face 3: 36 cm * 32 cm = 1152 cm² - Face 4: 36 cm * 32 cm = 1152 cm² - Face 5: 25 cm * 32 cm = 800 cm² - Face 6: 25 cm * 32 cm = 800 cm²

2. To find the surface area of the parallelepiped, we add up the areas of all six faces:

- Surface area of the parallelepiped = 900 cm² + 900 cm² + 1152 cm² + 1152 cm² + 800 cm² + 800 cm² = 5704 cm²

Therefore, the surface area of the rectangular parallelepiped is 5704 cm².

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