Question

Ребро куба дорівнює 5 см. Знайдіть діагональ куба, та діагональ бічної грані ​

Answer 1

Ответ:

5√3см

5√2см

Объяснение:

Диагональ куба находится по формуле:

D=a√3, где а- ребро куба.

D=5√3 см диагональ куба.

Диагональ квадрата находится по формуле:

d=a√2, где а -сторона квадрата (ребро куба)

d=a√2=5√2см

Answer 2

Ответ: 5√3 см; 5√2 см

Объяснение:

у куба все ребра равны. квадрат диагонали куба равен сумме квадратов трех его измерений. значит, если ребро 5, то диагональ равна

√(5²+5²+5²)=√75=√(25*3)=5√3/см/

диагональ боковой грани - это диагональ квадрата со стороной 5см, она, как известно, равна √(5²+5²)=√50=5√2/см/

Answer 3

Finding the Diagonal of a Cube

To find the diagonal of a cube, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In the case of a cube, the diagonal is the hypotenuse of a right triangle formed by two adjacent edges and a face diagonal. Let's denote the length of the edge of the cube as a.

Using the Pythagorean theorem, we can find the length of the diagonal of the cube (d) as follows:

d^2 = a^2 + a^2 + a^2

Simplifying the equation, we get:

d^2 = 3a^2

Taking the square root of both sides, we find:

d = sqrt(3a^2)

Given that the length of the edge of the cube is 5 cm, we can substitute a = 5 into the equation to find the length of the diagonal of the cube.

d = sqrt(3 * 5^2) = sqrt(3 * 25) = sqrt(75) ≈ 8.66 cm.

Finding the Diagonal of a Face of the Cube

To find the diagonal of a face of the cube, we can use the Pythagorean theorem again. In this case, the diagonal of a face is the hypotenuse of a right triangle formed by two adjacent edges.

Let's denote the length of the edge of the cube as a. The diagonal of a face (d_face) can be found using the Pythagorean theorem:

d_face^2 = a^2 + a^2

Simplifying the equation, we get:

d_face^2 = 2a^2

Taking the square root of both sides, we find:

d_face = sqrt(2a^2)

Substituting a = 5 into the equation, we can find the length of the diagonal of a face of the cube.

d_face = sqrt(2 * 5^2) = sqrt(2 * 25) = sqrt(50) ≈ 7.07 cm.

Therefore, the length of the diagonal of the cube is approximately 8.66 cm, and the length of the diagonal of a face of the cube is approximately 7.07 cm.

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