Calculate the number of blocks required to raise a rectangular building of two walls of length 100m, height of 10cm, and a distance of 4m between the walls. The building has a wind... Calculate the number of blocks required to raise a rectangular building of two walls of length 100m, height of 10cm, and a distance of 4m between the walls. The building has a window of 150cm x 1.5m. The brick size available is 45cm x 20cm. Consider the mortar space is 2% of the total area of the block wall. Read more

Steps to Solve

1. Calculate the total wall area

   First, we need to compute the area of one wall and then calculate the total area for two walls. Since there are two walls of length 100m and height 10cm:

   [ \text{Area of one wall} = \text{Length} \times \text{Height} = 100m \times 0.1m = 10m^2 ]

   The total area for two walls is:

   [ \text{Total wall area} = 2 \times 10m^2 = 20m^2 ]

2. Calculate the area of the window

   The window has dimensions of 150cm x 1.5m. We need to convert the window dimension of 150cm to meters:

   [ 150cm = 1.5m ]

   Now, calculate the area of the window:

   [ \text{Area of the window} = \text{Width} \times \text{Height} = 1.5m \times 1.5m = 2.25m^2 ]

3. Calculate the area of the walls without the window

   Now, we subtract the area of the window from the total wall area:

   [ \text{Net wall area} = \text{Total wall area} - \text{Area of the window} = 20m^2 - 2.25m^2 = 17.75m^2 ]

4. Calculate the total area considering mortar space

   The mortar space is 2% of the total wall area. Thus, we calculate it as follows:

   [ \text{Mortar area} = 0.02 \times \text{Net wall area} = 0.02 \times 17.75m^2 = 0.355m^2 ]

   Adding the mortar area back to the net wall area, we get the total area that needs to be covered with blocks:

   [ \text{Total area with mortar} = \text{Net wall area} + \text{Mortar area} = 17.75m^2 + 0.355m^2 = 18.105m^2 ]

5. Calculate the area of one block

   Each block has dimensions of 45cm x 20cm. First, convert these to meters:

   [ 45cm = 0.45m, \quad 20cm = 0.2m ]

   Now, calculate the area of one block:

   [ \text{Area of one block} = 0.45m \times 0.2m = 0.09m^2 ]

6. Calculate the number of blocks required

   Finally, determine the total number of blocks needed by dividing the total area with mortar by the area of one block:

   [ \text{Number of blocks} = \frac{\text{Total area with mortar}}{\text{Area of one block}} = \frac{18.105m^2}{0.09m^2} \approx 201.17 ]

   Since we cannot have a fraction of a block, round up to the nearest whole number:

   [ \text{Number of blocks} \approx 202 ]