A cube of side 4 cm is painted green on all its faces and then divided into smaller cubes of side 2 cm each. How many small cubes have been obtained?
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Understanding the Cube Division Problem
This problem involves a large cube that is cut into smaller identical cubes. To find the number of small cubes obtained, we can use the concept of volume. The total volume of the large cube remains constant, even when it's divided into smaller pieces. Therefore, the total volume is simply the sum of the volumes of all the smaller cubes.
Calculating the Volume of the Cubes
First, let's find the volume of the large cube. The side of the large cube is given as 4 cm.
Volume of a cube is calculated using the formula: \( \text{Volume} = \text{side}^3 \)
Volume of the large cube: \( (4 \text{ cm})^3 = 4 \times 4 \times 4 \text{ cm}^3 = 64 \text{ cm}^3 \)
Next, let's find the volume of one small cube. The side of each small cube is given as 2 cm.
Volume of a small cube: \( (2 \text{ cm})^3 = 2 \times 2 \times 2 \text{ cm}^3 = 8 \text{ cm}^3 \)
Finding the Number of Small Cubes
To find the total number of small cubes obtained, we divide the volume of the large cube by the volume of a single small cube.
Number of small cubes = \( \frac{\text{Volume of large cube}}{\text{Volume of small cube}} \)
Number of small cubes = \( \frac{64 \text{ cm}^3}{8 \text{ cm}^3} \)
Number of small cubes = \( 8 \)
Thus, when a cube of side 4 cm is divided into smaller cubes of side 2 cm each, 8 small cubes are obtained.
The information about the cube being painted green is relevant for problems asking about the number of cubes with painted faces (like 3 faces painted, 2 faces painted, etc.), but for finding the total number of small cubes, only the dimensions matter.
Important Questions from Cube and Dice
Three different positions of the same dice are shown, the six faces of which are numbered from 1 to 6. Select the number that will be on the face opposite to the one having '1'.
Pairs of adjacent sides of a big cube are coloured with red, yellow and brown colour. Now this big cube is divided into 64 small equal cubes. How many small cubes will have 3 faces painted with different colours?
Two adjacent faces of a solid cube are painted with black colour. The faces opposite to the black faces is painted with blue colour while the remaining faces are painted with yellow colour. After painting, this cube has been divided into 125 equal cubes. How many cubes have no faces painted?
A cube is painted blue on two adjacent faces and on one opposite face, green on two opposite faces and pink on the remaining face. It is then cut into 64 equal cubes. How many cubes have only one blue-coloured face?
A cube, whose two adjacent faces are coloured, is cut into 64 identical small cubes. How many of these small cubes are not coloured at all?
