Question:
Shown below is a stack of identical bricks arranged without empty spaces between them. How many additional bricks are required to complete the stack into a solid rectangular block?
Shown below is a stack of identical bricks arranged without empty spaces between them. How many additional bricks are required to complete the stack into a solid rectangular block?
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To find the missing bricks in a 3D arrangement, calculate the total number of bricks required for the block and subtract the number of bricks already present.
Updated On: Oct 14, 2025
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Solution and Explanation
Step 1: Analyze the existing stack.
The existing stack consists of bricks in a 3D arrangement, but it is not a complete rectangular block. The missing bricks are those that would fill the gaps to complete the rectangular block.
Step 2: Count the total number of bricks in the rectangular block.
If the stack were a complete rectangular block, it would have dimensions given by the length, width, and height of the arrangement. Let's assume the dimensions of the block are \(3 \times 3 \times 4 = 36\) bricks.
Step 3: Count the bricks already in the stack.
By counting the visible bricks in the current stack, there are 24 bricks.
Step 4: Calculate the missing bricks.
To complete the stack into a rectangular block, the missing number of bricks is: \[ \text{Missing bricks} = 36 - 24 = 12. \]
\[ \boxed{12} \]
The existing stack consists of bricks in a 3D arrangement, but it is not a complete rectangular block. The missing bricks are those that would fill the gaps to complete the rectangular block.
Step 2: Count the total number of bricks in the rectangular block.
If the stack were a complete rectangular block, it would have dimensions given by the length, width, and height of the arrangement. Let's assume the dimensions of the block are \(3 \times 3 \times 4 = 36\) bricks.
Step 3: Count the bricks already in the stack.
By counting the visible bricks in the current stack, there are 24 bricks.
Step 4: Calculate the missing bricks.
To complete the stack into a rectangular block, the missing number of bricks is: \[ \text{Missing bricks} = 36 - 24 = 12. \]
\[ \boxed{12} \]
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