Question

3 измерения прямоугольного параллелепипеда равны 5 см 7 см и 6см​

Answer 1

S поверхности = 2(5·7)+2(5·6)+2(7·6)=70+60+84=214(см²)

V = 5·7·6=210(см³).

Сумма длин всех рёбер = 5·4+6·4+7·4=20+24+28=72(см).

Всё, что можно сделать с этим.

Answer 2

Ответ:

210 см³ объём прямоугольного параллелепипеда

214 см² - площадь прямоугольного параллелепипеда

72 см - сумма длин всех рёбер прямоугольного параллелепипеда

11 см - длина диагонали  прямоугольного параллелепипеда

Пошаговое объяснение:

Что вычислить - не совсем понятно. Поэтому:

V = abc = 5*7*6 = 210 см³ - объём прямоугольного параллелепипеда

S = 2(ab + ac + bc)  = 2(5*7+5*6+6*7) = 2*107 = 214 см² - площадь прямоугольного параллелепипеда

L =  4(а + в + с) = 4(5+7+6) = 4*18 = 72 см - сумма длин всех рёбер прямоугольного параллелепипеда

d² = a² + b² + c²  

d = √a² + b² + c²  = √5²+7²+6² = √35+49+36 = √120 ≈ 11 см - длина диагонали  прямоугольного параллелепипеда

Answer 3

Dimensions of a Rectangular Parallelepiped

The dimensions of a rectangular parallelepiped are given as 5 cm, 7 cm, and 6 cm.

To clarify, a rectangular parallelepiped is a three-dimensional figure with six rectangular faces. It is also known as a rectangular prism.

Let's calculate some properties of this rectangular parallelepiped.

Surface Area

The surface area of a rectangular parallelepiped can be calculated by summing the areas of all six faces.

The formula for the surface area of a rectangular parallelepiped is:

Surface Area = 2(ab + bc + ac)

where a, b, and c are the lengths of the three sides of the parallelepiped.

In this case, the lengths are given as 5 cm, 7 cm, and 6 cm.

Using the formula, we can calculate the surface area:

Surface Area = 2(5 * 7 + 7 * 6 + 5 * 6) = 2(35 + 42 + 30) = 2(107) = 214 cm².

Therefore, the surface area of the given rectangular parallelepiped is 214 cm².

Volume

The volume of a rectangular parallelepiped can be calculated by multiplying the lengths of its three sides.

The formula for the volume of a rectangular parallelepiped is:

Volume = length * width * height

In this case, the lengths are given as 5 cm, 7 cm, and 6 cm.

Using the formula, we can calculate the volume:

Volume = 5 * 7 * 6 = 210 cm³.

Therefore, the volume of the given rectangular parallelepiped is 210 cm³.

Diagonals

The diagonals of a rectangular parallelepiped can be calculated using the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

For a rectangular parallelepiped, there are three diagonals: the body diagonal, the face diagonal, and the space diagonal.

- The body diagonal connects opposite corners of the parallelepiped. - The face diagonal connects opposite corners of a face. - The space diagonal connects opposite corners of the parallelepiped, passing through the interior.

To calculate the length of the body diagonal, we can use the formula:

Body Diagonal = √(a² + b² + c²)

where a, b, and c are the lengths of the three sides of the parallelepiped.

In this case, the lengths are given as 5 cm, 7 cm, and 6 cm.

Using the formula, we can calculate the body diagonal:

Body Diagonal = √(5² + 7² + 6²) = √(25 + 49 + 36) = √110 = 10.49 cm.

To calculate the length of the face diagonal, we can use the formula:

Face Diagonal = √(a² + b²)

where a and b are the lengths of two sides of a face.

In this case, the lengths are given as 5 cm and 7 cm.

Using the formula, we can calculate the face diagonal:

Face Diagonal = √(5² + 7²) = √(25 + 49) = √74 = 8.60 cm.

To calculate the length of the space diagonal, we can use the formula:

Space Diagonal = √(a² + b² + c²)

where a, b, and c are the lengths of the three sides of the parallelepiped.

In this case, the lengths are given as 5 cm, 7 cm, and 6 cm.

Using the formula, we can calculate the space diagonal:

Space Diagonal = √(5² + 7² + 6²) = √(25 + 49 + 36) = √110 = 10.49 cm.

Therefore, the length of the body diagonal, face diagonal, and space diagonal of the given rectangular parallelepiped are approximately 10.49 cm, 8.60 cm, and 10.49 cm, respectively.

I hope this helps! Let me know if you have any further questions.