Question

While playing with blocks, Tim wants to form a cube using rectangular prisms with the given dimensions. Which of the following is the correct number of blocks that will be required?

• A. 36
• B. 18
• C. 6
• D. 12

Answer 1

The correct option is A 36


As Tim wants to form a cube, the length, width, and height of the shape should be the same.
Length of the block = 3 in


If we want the width of the block to be equal to length, we will need more than one block.
Taking the common multiple of 2 and $3=2\times 3=6$

To find the number of blocks required to form a cube with equal length, width and height,
Length of one block = 3 in $\Rightarrow$ 2 blocks are required to form a length equivalent to 6 in.
Width of one block = 2 in $\Rightarrow$ 3 blocks are required to form a width equivalent to 6 in.
Height of one block = 1 in $\Rightarrow$ 6 blocks are required to form a height equivalent to 6 in.
Number of blocks required to form the base of the cube = number of blocks along the length $\times$ number of blocks along the width
$=2\times 3=6$
Total number of blocks required to form the cube = number of blocks required to form the base $\times$ number of blocks along the height
$=6\times 6=36$ blocks
Thus, Tim will need 36 blocks to form a cube.