Question

СРОЧНО 100 балів !!!!!Зобразiть куб, ребро якого дорівнює 4 см. Проведіть діагоналі однієї основи і однієї бічної грані. Знайдіть їх довжини. Побудуйте діагональ куба і знайдіть її довжину.​

Answer 1

Ответ:

Діагональ бічної грані=√(4²+4²)=√32=4/2

Діагональ куба=√(4²+(4√2)²)=√48=4√3

Объяснение:

Наче так

Answer 2

To answer your question, let's break it down into steps:

1. Drawing the cube: Start by drawing a square with each side measuring 4 cm. This square will represent the base of the cube. Then, draw four vertical lines extending from each corner of the square to meet at a point above the square. Connect the top ends of these lines to form another square. Finally, draw lines connecting the corresponding corners of the two squares to complete the cube.

2. Finding the length of the diagonals: To find the length of the diagonals, we need to consider the right triangles formed by the diagonals and the sides of the cube. Since the sides of the cube are all equal, these triangles are isosceles right triangles. In an isosceles right triangle, the length of the hypotenuse (diagonal) can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the other two sides of the isosceles right triangle are the sides of the cube, which measure 4 cm each. Applying the Pythagorean theorem, we can find the length of the diagonal:

Diagonal = √(4^2 + 4^2) = √(16 + 16) = √32 cm ≈ 5.66 cm.

3. Drawing and finding the length of the diagonal of the cube: To draw the diagonal of the cube, we need to connect two opposite vertices of the cube. This diagonal will pass through the center of the cube. To find its length, we can again use the Pythagorean theorem.

The length of the diagonal can be found by considering a right triangle formed by the diagonal, one side of the cube, and the diagonal of one face of the cube. The diagonal of one face of the cube is equal to the side length of the cube, which is 4 cm.

Applying the Pythagorean theorem, we can find the length of the diagonal of the cube:

Diagonal = √(4^2 + 4^2 + 4^2) = √(16 + 16 + 16) = √48 cm ≈ 6.93 cm.

So, the length of the diagonals of one base and one lateral face of the cube is approximately 5.66 cm, and the length of the diagonal of the cube is approximately 6.93 cm.

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