Let's break down the problem using the dimensions provided:

1. The block has the following dimensions:

   • Height = 900 mm = 90 cm (since 1 mm = 0.1 cm)
   • Length = 1.8 m = 180 cm (since 1 m = 100 cm)
   • Width = 36 cm

2. Joe wants to cut cubes with side lengths of 18 cm from this block.

3. To determine how many cubes of 18 cm side length can fit into the block, we need to divide each dimension of the block by the side length of the cube (18 cm):

   • Along the height: $\frac{90 \, \text{cm}}{18 \, \text{cm}} = 5$
   • Along the length: $\frac{180 \, \text{cm}}{18 \, \text{cm}} = 10$
   • Along the width: $\frac{36 \, \text{cm}}{18 \, \text{cm}} = 2$

4. Now, multiply these results to find the total number of cubes:

   • $5 \times 10 \times 2 = 100$

Thus, Joe can cut 100 cubes from the block, which corresponds to option (C).

Would you like any more details or have any questions? Here are 5 related questions to expand your understanding:

1. What is the formula for calculating the volume of a rectangular block?
2. How would the result change if the cube's side length were different?
3. Can the volume of the block be used to verify the answer in another way?
4. How would cutting the block diagonally affect the number of cubes?
5. If some cubes were imperfect due to cutting errors, how might this change the total count?

Tip: Always make sure to convert all measurements into the same unit before performing any calculations!