Question

Shape A has twice the number of cubes as Shape B. But the dimensions of the cubes in Shape B are twice the dimensions of the cubes in Shape A. Compare the volume of the shapes.

• A. Volumes of shapes A and B are equal
• B. Volume of Shape A is greater
• C. None of the above
• D. Volume of Shape B is greater

Answer 1

The correct option is D Volume of Shape B is greater

Given, the length of each cube of Shape $A=1$ cm
Volume of each cube in Shape $A=1\times 1\times 1=1$ cu cm
Number of cubes in Shape $A=$ Number of cubes in the base layer $\times$ Number of layers $=(4\times 2)\times 2$ $=8\times 2=16$ cubes

Volume of Shape $A=$ Volume of $1$ unit cube $\times$ Number of cubes in the shape $=1\times 16=16$ cu cm

Given, the length of each cube of Shape $B=2$ cm
Volume of each cube in Shape $B=2\times 2\times 2=8$ cu cm
Number of cubes in Shape $B=$ Number of cubes in the base layer $\times$ Number of layers $=(2\times 2)\times 2=4\times 2=8$ cubes
Volume of Shape $B=$ Volume of $1$ unit cube $\times$ Number of cubes in the shape $=8\times 8=64$ cu cm

Clearly, $64$ cu cm $>16$ cu cm
Therefore, though the number of cubes in Shape $A$ is more, the volume of Shape $B$ is greater.