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How many blocks are in a cube?

Understand the Problem

The question is asking about the number of smaller blocks that can fit into a cube, which is a concept in geometry. To approach this, we would need to know the size of the smaller blocks and the dimensions of the cube itself to calculate how many can fit.

Answer

The number of smaller blocks that can fit into the cube is given by $N = \left( \frac{L}{s} \right)^3$.
Answer for screen readers

The number of smaller blocks that can fit into a cube is given by:

$$ N = \left( \frac{L}{s} \right)^3 $$

Steps to Solve

  1. Identify the dimensions of the cube and the block

Assume the cube has a side length of $L$ and the smaller block has a side length of $s$.

  1. Calculate the volume of the cube

The volume $V_{cube}$ of the cube can be calculated using the formula:

$$ V_{cube} = L^3 $$

  1. Calculate the volume of one smaller block

The volume $V_{block}$ of one smaller block can be calculated using the formula:

$$ V_{block} = s^3 $$

  1. Determine how many smaller blocks fit into the cube

To find out how many smaller blocks fit into the cube, divide the volume of the cube by the volume of one smaller block:

$$ N = \frac{V_{cube}}{V_{block}} = \frac{L^3}{s^3} $$

  1. Simplify the expression

This can be further simplified to find the number of blocks that fit:

$$ N = \left( \frac{L}{s} \right)^3 $$

  1. Final answer

If you know the specific values for $L$ and $s$, substitute them in to find the exact number of smaller blocks that can fit in the cube.

The number of smaller blocks that can fit into a cube is given by:

$$ N = \left( \frac{L}{s} \right)^3 $$

More Information

In this problem, it is assumed that the smaller blocks are perfectly cuboidal and fit without leaving any gaps. This calculation represents a fundamental concept in geometry known as volume packing in three-dimensional space.

Tips

  • Forgetting to cube the side lengths of the blocks and the cube. Ensure that volume is calculated as $L^3$ for the cube and $s^3$ for the block.
  • Not simplifying the final expression correctly. It is important to use the ratio $\frac{L}{s}$ and cube it to find the correct number of blocks.
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