Calculate the number of blocks required to raise a rectangular building of two walls of length 100m, and the height of 10cm. While the length between one side wall to another is 4m... Calculate the number of blocks required to raise a rectangular building of two walls of length 100m, and the height of 10cm. While the length between one side wall to another is 4m. The building has 8 windows of 150cm x 1.5m. The brick size available is 45cm x 20cm. Consider the mortar space is 2% of total area of the block wall.
Understand the Problem
The question is asking to calculate the number of blocks required to raise two walls of a building with specified dimensions and taking into account the area of windows and mortar space. The calculation will involve determining the area of the walls and adjusting for windows and the mortar space.
Answer
The number of blocks required is 23.
Answer for screen readers
The number of blocks required to raise the walls is 23.
Steps to Solve
- Calculate Total Wall Area
The building has two walls, each with a length of 100 m and height of 10 cm (0.1 m).
The area of one wall is: $$ A = \text{length} \times \text{height} = 100 \text{ m} \times 0.1 \text{ m} = 10 \text{ m}^2 $$
Total area for two walls: $$ \text{Total Wall Area} = 2 \times 10 \text{ m}^2 = 20 \text{ m}^2 $$
- Calculate Total Area for Windows
There are 8 windows, each measuring 150 cm x 150 cm (1.5 m x 1.5 m).
The area of one window is: $$ \text{Area}_{\text{window}} = 1.5 \text{ m} \times 1.5 \text{ m} = 2.25 \text{ m}^2 $$
Total area for all windows: $$ \text{Total Window Area} = 8 \times 2.25 \text{ m}^2 = 18 \text{ m}^2 $$
- Calculate Net Wall Area After Windows
Now we subtract the total window area from the total wall area: $$ \text{Net Wall Area} = \text{Total Wall Area} - \text{Total Window Area} $$ $$ \text{Net Wall Area} = 20 \text{ m}^2 - 18 \text{ m}^2 = 2 \text{ m}^2 $$
- Adjust for Mortar Space
We need to account for the mortar space, which is 2% of the total area of the block wall: $$ \text{Mortar Area} = 0.02 \times \text{Net Wall Area} = 0.02 \times 2 \text{ m}^2 = 0.04 \text{ m}^2 $$
The adjusted wall area is: $$ \text{Adjusted Wall Area} = \text{Net Wall Area} + \text{Mortar Area} = 2 \text{ m}^2 + 0.04 \text{ m}^2 = 2.04 \text{ m}^2 $$
- Calculate Block Area
The size of each block is 45 cm x 20 cm, which we convert to meters: $$ 45 \text{ cm} = 0.45 \text{ m}, \quad 20 \text{ cm} = 0.2 \text{ m} $$
Now, calculate the area of one block: $$ \text{Area}_{\text{block}} = 0.45 \text{ m} \times 0.2 \text{ m} = 0.09 \text{ m}^2 $$
- Calculate Number of Blocks Needed
Finally, divide the adjusted wall area by the area of one block: $$ \text{Number of Blocks} = \frac{\text{Adjusted Wall Area}}{\text{Area}_{\text{block}}} = \frac{2.04 \text{ m}^2}{0.09 \text{ m}^2} \approx 22.67 $$
Since you can't have a fraction of a block, round up to the nearest whole number: $$ \text{Number of Blocks Required} = 23 $$
The number of blocks required to raise the walls is 23.
More Information
In construction, it's important to accommodate for factors like window spaces and mortar when calculating material requirements. In this case, adjusting for the mortar space is crucial as it affects the amount of material needed.
Tips
- Not converting units: Failing to convert all measurements into the same unit (e.g., cm to m) can lead to inaccurate calculations.
- Ignoring window areas: Forgetting to subtract the area of windows from the wall area will lead to overestimating the number of blocks needed.
- Not rounding up: Always round up when calculating the number of blocks needed, as you can't purchase a fraction of a block.
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