Question

A cube is formed by joining unit cubes of different colors. Compare the volume of the yellow, green, and red layers, and select the option with the correct answer.

• A. The sum of the volume of the red and green layers is equal to the yellow layer
• B. The sum of the volume of the red and green layers is less than the yellow layer
• C. We cannot compare the volume of layers of different shapes
• D. The sum of the volume of the red and green layers is greater than the yellow layer

Answer 1

The correct option is A The sum of the volume of the red and green layers is equal to the yellow layer

For all three colors,
Length of each small cube $=1$ cm
Volume of the cube $=1\times 1\times 1=1$ cu cm

For the red layer,
Number of cubes in the base of the red layer $=3\times 1=3$
Volume of one layer $=$ Volume of 1 unit cube $\times$ Number of cubes in the layer $=1\times 3=3$ cu cm
Total volume of the red layer $=$ Volume of 1 layer $\times$ Number of layers $=3\times 2=6$ cu cm

For the green layer,
Number of cubes in the base of the green layer $=3\times 1=3$ cubes
Volume of one layer $=$ Volume of $1$ unit cube $\times$ Number of cubes in the layer $=1\times 3=3$ cu cm
Total volume of the green layer $=$ Volume of $1$ layer $\times$ Number of layers $=3\times 2=6$ cu cm

For the yellow layer,
Number of cubes in the base of the yellow layer $=3\times 1=3$ cubes
Volume of one layer $=$ Volume of 1 unit cube $\times$ Number of cubes in the layer $=1\times 3=3$ cu units
Total volume of the yellow layer $=$ Volume of $1$ layer $\times$ Number of layers $=3\times 4=12$ cu units

Sum of the volume of the red and green layers $=6+6=12=$ Total volume of the yellow layer
Therefore, the sum of the volume of the red and green layers is equal to the yellow layer.
Thus, Option C is correct.