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Sagot :
To determine the number of bricks needed to construct the wall, we need to carry out the following steps:
1. Convert the dimensions of the wall to consistent units (centimeters):
- Wall length: 33 meters = 33 100 cm = 3300 cm
- Wall height: 3.5 meters = 3.5 100 cm = 350 cm
- Wall thickness: 40 cm (already in centimeters)
2. Calculate the volume of the wall (in cubic centimeters):
The volume [tex]\( V \)[/tex] of a rectangular solid (wall) is given by:
[tex]\[ V_{\text{wall}} = \text{length} \times \text{height} \times \text{thickness} \][/tex]
Substituting the values:
[tex]\[ V_{\text{wall}} = 3300 \, \text{cm} \times 350 \, \text{cm} \times 40 \, \text{cm} = 46200000 \, \text{cm}^3 \][/tex]
3. Calculate the volume of one brick (in cubic centimeters):
The volume [tex]\( V \)[/tex] of a brick is given by:
[tex]\[ V_{\text{brick}} = \text{length} \times \text{width} \times \text{height} \][/tex]
Given the dimensions of the brick:
[tex]\[ V_{\text{brick}} = 22 \, \text{cm} \times 10 \, \text{cm} \times 7 \, \text{cm} = 1540 \, \text{cm}^3 \][/tex]
4. Determine the usable volume of the wall for bricks (considering 1/10 part occupied by cement and sand):
Only 9/10 of the wall's volume will be occupied by bricks:
[tex]\[ V_{\text{usable wall}} = V_{\text{wall}} \times \frac{9}{10} \][/tex]
Substituting the volume of the wall:
[tex]\[ V_{\text{usable wall}} = 46200000 \, \text{cm}^3 \times \frac{9}{10} = 41580000 \, \text{cm}^3 \][/tex]
5. Calculate the number of bricks needed:
The number of bricks can be determined by dividing the usable volume of the wall by the volume of one brick:
[tex]\[ \text{Number of bricks} = \frac{V_{\text{usable wall}}}{V_{\text{brick}}} \][/tex]
Substituting the values:
[tex]\[ \text{Number of bricks} = \frac{41580000 \, \text{cm}^3}{1540 \, \text{cm}^3} = 27000 \, \text{bricks} \][/tex]
Therefore, the number of bricks required to construct the wall is [tex]\(\boxed{27000}\)[/tex].
So, the correct option is:
(a) 27000
1. Convert the dimensions of the wall to consistent units (centimeters):
- Wall length: 33 meters = 33 100 cm = 3300 cm
- Wall height: 3.5 meters = 3.5 100 cm = 350 cm
- Wall thickness: 40 cm (already in centimeters)
2. Calculate the volume of the wall (in cubic centimeters):
The volume [tex]\( V \)[/tex] of a rectangular solid (wall) is given by:
[tex]\[ V_{\text{wall}} = \text{length} \times \text{height} \times \text{thickness} \][/tex]
Substituting the values:
[tex]\[ V_{\text{wall}} = 3300 \, \text{cm} \times 350 \, \text{cm} \times 40 \, \text{cm} = 46200000 \, \text{cm}^3 \][/tex]
3. Calculate the volume of one brick (in cubic centimeters):
The volume [tex]\( V \)[/tex] of a brick is given by:
[tex]\[ V_{\text{brick}} = \text{length} \times \text{width} \times \text{height} \][/tex]
Given the dimensions of the brick:
[tex]\[ V_{\text{brick}} = 22 \, \text{cm} \times 10 \, \text{cm} \times 7 \, \text{cm} = 1540 \, \text{cm}^3 \][/tex]
4. Determine the usable volume of the wall for bricks (considering 1/10 part occupied by cement and sand):
Only 9/10 of the wall's volume will be occupied by bricks:
[tex]\[ V_{\text{usable wall}} = V_{\text{wall}} \times \frac{9}{10} \][/tex]
Substituting the volume of the wall:
[tex]\[ V_{\text{usable wall}} = 46200000 \, \text{cm}^3 \times \frac{9}{10} = 41580000 \, \text{cm}^3 \][/tex]
5. Calculate the number of bricks needed:
The number of bricks can be determined by dividing the usable volume of the wall by the volume of one brick:
[tex]\[ \text{Number of bricks} = \frac{V_{\text{usable wall}}}{V_{\text{brick}}} \][/tex]
Substituting the values:
[tex]\[ \text{Number of bricks} = \frac{41580000 \, \text{cm}^3}{1540 \, \text{cm}^3} = 27000 \, \text{bricks} \][/tex]
Therefore, the number of bricks required to construct the wall is [tex]\(\boxed{27000}\)[/tex].
So, the correct option is:
(a) 27000
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