To construct a wall 18 m long, 0.5 m thick and 9 m high, bricks of dimensions `20 cm xx 15 cm xx 10 cm` each are used. If the mortar occupies `1//10^(th)` of the volume of the wall, then find the number of bricks used.

Options

A. 32960
B. 24420
C. 24300
D. 24296

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the volume of the wall.
The volume \( V \) of the wall can be calculated using the formula:
\[ V = \text{length} \times \text{thickness} \times \text{height} \]
Given:
- Length = 18 m
- Thickness = 0.5 m
- Height = 9 m

Substituting the values:
\[ V = 18 \, \text{m} \times 0.5 \, \text{m} \times 9 \, \text{m} = 81 \, \text{m}^3 \]

### Step 2: Calculate the volume occupied by the mortar.
According to the problem, the mortar occupies \( \frac{1}{10} \) of the volume of the wall. Therefore, the volume occupied by the mortar \( V_m \) is:
\[ V_m = \frac{1}{10} \times V = \frac{1}{10} \times 81 \, \text{m}^3 = 8.1 \, \text{m}^3 \]

### Step 3: Calculate the volume of bricks used.
The volume of bricks \( V_b \) used in the wall can be calculated by subtracting the volume occupied by the mortar from the total volume of the wall:
\[ V_b = V - V_m = 81 \, \text{m}^3 - 8.1 \, \text{m}^3 = 72.9 \, \text{m}^3 \]

### Step 4: Convert the volume of bricks to cubic centimeters.
Since the dimensions of the bricks are given in centimeters, we need to convert the volume of bricks from cubic meters to cubic centimeters.
1 cubic meter = \( 10^6 \) cubic centimeters, so:
\[ V_b = 72.9 \, \text{m}^3 \times 10^6 \, \text{cm}^3/\text{m}^3 = 72,900,000 \, \text{cm}^3 \]

### Step 5: Calculate the volume of one brick.
The volume \( V_{brick} \) of one brick can be calculated as:
\[ V_{brick} = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the brick:
- Length = 20 cm
- Width = 15 cm
- Height = 10 cm

Substituting the values:
\[ V_{brick} = 20 \, \text{cm} \times 15 \, \text{cm} \times 10 \, \text{cm} = 3000 \, \text{cm}^3 \]

### Step 6: Calculate the number of bricks used.
The number of bricks \( N \) used can be calculated by dividing the total volume of bricks by the volume of one brick:
\[ N = \frac{V_b}{V_{brick}} = \frac{72,900,000 \, \text{cm}^3}{3000 \, \text{cm}^3} = 24300 \]

### Final Answer:
The number of bricks used to construct the wall is **24,300**.