We are given a rectangular block of wood with the dimensions as follows:

• 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

Joe wants to cut this block into cubes, each with side lengths of 18 cm.

Step 1: Calculate the volume of the rectangular block.

The volume $V_{\text{block}}$ of a rectangular block is given by: $V_{\text{block}} = \text{Length} \times \text{Width} \times \text{Height}$ Substituting the given dimensions (all in cm): $V_{\text{block}} = 180 \, \text{cm} \times 36 \, \text{cm} \times 90 \, \text{cm} = 583200 \, \text{cm}^3$

Step 2: Calculate the volume of one cube.

The volume $V_{\text{cube}}$ of a cube is given by: $V_{\text{cube}} = \text{side length}^3$ Substituting the side length of 18 cm: $V_{\text{cube}} = 18 \, \text{cm} \times 18 \, \text{cm} \times 18 \, \text{cm} = 5832 \, \text{cm}^3$

Step 3: Determine how many cubes fit into the block.

To find how many cubes Joe can cut from the block, divide the volume of the block by the volume of one cube: $\text{Number of cubes} = \frac{V_{\text{block}}}{V_{\text{cube}}} = \frac{583200 \, \text{cm}^3}{5832 \, \text{cm}^3} = 100$

Thus, Joe can cut 100 cubes from the block.

The correct answer is (C) 100.

Would you like any further details or explanations on any part of the solution?

Here are 5 related questions to deepen understanding:

1. What is the formula for the volume of a cube?
2. How do you convert between different units of measurement, such as meters to centimeters?
3. Can Joe cut cubes with a side length of 15 cm instead? How many would fit?
4. What happens if the dimensions of the block change? How does this affect the number of cubes?
5. What other shapes could Joe cut from the block, and how would you calculate those?

Tip: Always make sure all units are consistent before performing calculations to avoid errors.