Question

Сумма длин всех рёбер куба равна 60 см. Найдите площадь поверхности куба.

Answer 1

1)60/12 граней=5
2)S=6H^2=6*25=125

Answer 2

Рёбер в кубе 12
длина одного ребра равна 60/12=5см=a
площадь куба P=6*a^2
P=6*5^2=150cм2

Answer 3

Finding the Length of the Cube's Edges

To find the surface area of a cube, we first need to determine the length of its edges. The problem states that the sum of the lengths of all the edges of the cube is 60 cm.

Let's assume the length of each edge of the cube is x cm. Since a cube has 12 edges, the sum of the lengths of all the edges can be expressed as:

12 * x = 60

Simplifying the equation, we can solve for x:

x = 60 / 12 x = 5 cm

Therefore, each edge of the cube is 5 cm long.

Calculating the Surface Area of the Cube

The surface area of a cube can be calculated by finding the area of one face and then multiplying it by 6, as a cube has 6 equal faces.

The area of one face of the cube is given by the formula:

Area = side length * side length

Since each side length is 5 cm, the area of one face is:

Area = 5 cm * 5 cm Area = 25 cm^2

To find the total surface area of the cube, we multiply the area of one face by 6:

Total Surface Area = 6 * Area Total Surface Area = 6 * 25 cm^2 Total Surface Area = 150 cm^2

Therefore, the surface area of the cube is 150 square centimeters.