How many brick ( number near to next hundred ) will be required to build a wall 30 m long , 30 cm thick and 5 m high with a provision of 2 doors , each ` 4 m xx 2.5 m ` and each brick being ` 20 cm xx 16 cm xx 8 cm ` when one-ninth of the wall is filled with lime ?

Options

A. a. 13500 bricks
B. b. 13600 bricks
C. c. 20050 bricks
D. d. 18500 bricks

Answer

To solve the problem of how many bricks are required to build a wall with given dimensions and specifications, we will follow these steps:

### Step 1: Calculate the volume of the wall
The volume of the wall can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given:
- Length (L) = 30 m
- Breadth (B) = 30 cm = 0.3 m (conversion from cm to m)
- Height (H) = 5 m

Now substituting the values:
\[ \text{Volume of the wall} = 30 \, \text{m} \times 0.3 \, \text{m} \times 5 \, \text{m} \]
\[ \text{Volume of the wall} = 45 \, \text{m}^3 \]

### Step 2: Calculate the volume of the doors
Each door has dimensions:
- Width = 4 m
- Height = 2.5 m

The area of one door:
\[ \text{Area of one door} = 4 \, \text{m} \times 2.5 \, \text{m} = 10 \, \text{m}^2 \]

Since there are 2 doors:
\[ \text{Total area of doors} = 2 \times 10 \, \text{m}^2 = 20 \, \text{m}^2 \]

Now, to find the volume of the doors, we need to multiply the area by the thickness of the wall:
\[ \text{Volume of doors} = \text{Total area of doors} \times \text{Thickness} \]
\[ \text{Volume of doors} = 20 \, \text{m}^2 \times 0.3 \, \text{m} = 6 \, \text{m}^3 \]

### Step 3: Calculate the effective volume of the wall
Now, we subtract the volume of the doors from the volume of the wall:
\[ \text{Effective volume of the wall} = \text{Volume of the wall} - \text{Volume of doors} \]
\[ \text{Effective volume of the wall} = 45 \, \text{m}^3 - 6 \, \text{m}^3 = 39 \, \text{m}^3 \]

### Step 4: Calculate the volume filled with lime
According to the problem, one-ninth of the effective volume of the wall is filled with lime:
\[ \text{Volume filled with lime} = \frac{1}{9} \times 39 \, \text{m}^3 = 4.33 \, \text{m}^3 \]

### Step 5: Calculate the volume available for bricks
Now, we subtract the volume filled with lime from the effective volume of the wall:
\[ \text{Volume available for bricks} = \text{Effective volume of the wall} - \text{Volume filled with lime} \]
\[ \text{Volume available for bricks} = 39 \, \text{m}^3 - 4.33 \, \text{m}^3 = 34.67 \, \text{m}^3 \]

### Step 6: Calculate the volume of one brick
The dimensions of one brick are:
- Length = 20 cm = 0.2 m
- Width = 16 cm = 0.16 m
- Height = 8 cm = 0.08 m

Now, calculate the volume of one brick:
\[ \text{Volume of one brick} = 0.2 \, \text{m} \times 0.16 \, \text{m} \times 0.08 \, \text{m} \]
\[ \text{Volume of one brick} = 0.00256 \, \text{m}^3 \]

### Step 7: Calculate the number of bricks required
To find the number of bricks, divide the volume available for bricks by the volume of one brick:
\[ \text{Number of bricks} = \frac{\text{Volume available for bricks}}{\text{Volume of one brick}} \]
\[ \text{Number of bricks} = \frac{34.67 \, \text{m}^3}{0.00256 \, \text{m}^3} \approx 13500 \]

### Step 8: Round to the nearest hundred
The nearest hundred to 13500 is 13500 itself.

### Final Answer
The number of bricks required is approximately **13500**.

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