Marble Block Volume Calculation

First, we need to find the total volume of the marble block. The dimensions of the block are given as 5 m, 4 m, and 2 m.

The formula for the volume of a rectangular block (cuboid) is length × width × height.

So, the volume of the marble block ($V_{block}$) is: $V_{block} = 5 \, \text{m} \times 4 \, \text{m} \times 2 \, \text{m}$ $V_{block} = 40 \, \text{m}^3$

Tile Volume Calculation

Next, we calculate the volume of a single rectangular tile. The dimensions are 1 m × 0.5 m with a thickness of 10 cm.

We must ensure all dimensions are in the same unit. Let's convert the thickness from centimeters to meters: $10 \, \text{cm} = \frac{10}{100} \, \text{m} = 0.1 \, \text{m}$

The volume of one tile ($V_{tile}$) is: $V_{tile} = 1 \, \text{m} \times 0.5 \, \text{m} \times 0.1 \, \text{m}$ $V_{tile} = 0.05 \, \text{m}^3$

Wastage Effect on Volume

The problem states that there is a 10% wastage in cutting. This means that only 90% of the total marble block volume is actually usable for making tiles.

To find the usable volume ($V_{usable}$), we calculate 90% of the total block volume: $V_{usable} = V_{block} \times (100\% - 10\%)$ $V_{usable} = 40 \, \text{m}^3 \times 90\%$ $V_{usable} = 40 \, \text{m}^3 \times \frac{90}{100}$ $V_{usable} = 40 \, \text{m}^3 \times 0.90$ $V_{usable} = 36 \, \text{m}^3$

Number of Tiles Calculation

Finally, to find the total number of tiles that can be made, we divide the usable volume of the marble by the volume of a single tile.

Number of tiles = $\frac{V_{usable}}{V_{tile}}$

Number of tiles = $\frac{36 \, \text{m}^3}{0.05 \, \text{m}^3}$

Number of tiles = $\frac{36}{0.05}$

To simplify the division, we can multiply the numerator and denominator by 100: Number of tiles = $\frac{36 \times 100}{0.05 \times 100} = \frac{3600}{5}$

Number of tiles = 720

Therefore, 720 tiles will be made from the block of marble, considering the 10% wastage.