Question

Зелёный деревянный кубик с ребром 3см распилили на квадратные сантиметры. сколько получилось кубиков,окрашенных с трёх сторон? С двух сторон? С одной стороны?

Answer 1

Calculation of Cubes Painted on Three Sides

To determine the number of cubes that are painted on three sides, we need to calculate the number of square centimeters obtained from the wooden cube and divide it by the area of one face of the cube.

Given that the wooden cube has an edge length of 3 cm, the total surface area of the cube can be calculated as follows:

Surface Area of Cube = 6 * (Edge Length)^2

Substituting the value of the edge length, we get:

Surface Area of Cube = 6 * (3 cm)^2 = 54 square centimeters

Now, we need to determine the number of square centimeters that can be obtained from one face of the cube. Since each face of the cube is a square, the area of one face is equal to the edge length squared:

Area of One Face = (Edge Length)^2 = (3 cm)^2 = 9 square centimeters

To find the number of cubes that are painted on three sides, we divide the total surface area of the cube by the area of one face:

Number of Cubes Painted on Three Sides = Surface Area of Cube / Area of One Face

Number of Cubes Painted on Three Sides = 54 square centimeters / 9 square centimeters = 6 cubes

Therefore, the number of cubes that are painted on three sides is 6.

Calculation of Cubes Painted on Two Sides

To determine the number of cubes that are painted on two sides, we need to consider the number of cubes that are not painted on three sides. Since we have already calculated that there are 6 cubes painted on three sides, we subtract this number from the total number of cubes.

Total Number of Cubes = Number of Cubes Painted on Three Sides + Number of Cubes Not Painted on Three Sides

Total Number of Cubes = 6 cubes + Number of Cubes Not Painted on Three Sides

Since the wooden cube was divided into smaller square centimeters, the remaining cubes that are not painted on three sides will have at least one face that is not painted. Therefore, the number of cubes painted on two sides is equal to the number of cubes not painted on three sides.

Number of Cubes Painted on Two Sides = Number of Cubes Not Painted on Three Sides

Number of Cubes Painted on Two Sides = Total Number of Cubes - Number of Cubes Painted on Three Sides

Number of Cubes Painted on Two Sides = Total Number of Cubes - 6 cubes

Since we don't have the information about the total number of cubes, we cannot determine the exact number of cubes painted on two sides. However, we can say that the number of cubes painted on two sides is less than or equal to the total number of cubes.

Calculation of Cubes Painted on One Side

To determine the number of cubes that are painted on one side, we need to consider the number of cubes that are not painted on two or three sides. Since we don't have the information about the total number of cubes, we cannot determine the exact number of cubes painted on one side.

However, we can say that the number of cubes painted on one side is equal to the total number of cubes minus the number of cubes painted on two sides and the number of cubes painted on three sides.

Number of Cubes Painted on One Side = Total Number of Cubes - Number of Cubes Painted on Two Sides - Number of Cubes Painted on Three Sides

Since we don't have the information about the total number of cubes, we cannot provide an exact answer for the number of cubes painted on one side.

In summary: - The number of cubes painted on three sides is 6. - The number of cubes painted on two sides is less than or equal to the total number of cubes. - The number of cubes painted on one side cannot be determined without the total number of cubes.