Question

Площадь полной поверхности куба равна 60 см2 найдите длину диагонали грани куба

Answer 1

60 : 6 =10 площадь грани куба, ребро куба = корню кв. из 10. По т. Пифагора найдем диагональ грани 10+ 10 = d^2   d = корню из 20 или 2 умножить на корень и5

Answer 2

Finding the Length of the Diagonal of a Cube

To find the length of the diagonal of a cube, we can use the formula:

Diagonal length = Edge length * √3

Given that the total surface area of the cube is 60 cm², we can find the edge length using the formula:

Surface area = 6 * (Edge length)²

Let's calculate the edge length first:

60 cm² = 6 * (Edge length)²

Dividing both sides by 6, we get:

10 cm² = (Edge length)²

Taking the square root of both sides, we find:

Edge length = √10 cm

Now, we can calculate the length of the diagonal:

Diagonal length = √3 * √10 cm

Simplifying, we have:

Diagonal length = √30 cm

Therefore, the length of the diagonal of the cube is √30 cm.