The cross section of a canal is in the shape of an isosceles trapezium which is 4 metre wide at the bottom and 5 metre wide at the top. If the depth of the canal is 2 metre and it is 120 metre long, what is the maximum capacity of this canal ?

Options

A. 2160 cubic metre
B. 3240 cubic metre
C. 4320 cubic metre
D. 1080 cubic metre

Answer

To find the maximum capacity of the canal, we need to calculate the volume of the canal, which can be determined by finding the area of the cross-section (which is in the shape of an isosceles trapezium) and then multiplying it by the length of the canal.

### Step-by-Step Solution:

1. **Identify the dimensions of the trapezium**:
- Width at the bottom (a) = 4 meters
- Width at the top (b) = 5 meters
- Height (h) = 2 meters

2. **Use the formula for the area of a trapezium**:
The area \( A \) of a trapezium is given by the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
where \( a \) and \( b \) are the lengths of the parallel sides and \( h \) is the height.

3. **Substitute the values into the formula**:
\[ A = \frac{1}{2} \times (4 + 5) \times 2 \]
\[ A = \frac{1}{2} \times 9 \times 2 \]
\[ A = \frac{1}{2} \times 18 = 9 \text{ m}^2 \]

4. **Calculate the volume of the canal**:
The volume \( V \) can be calculated by multiplying the area of the trapezium by the length of the canal.
\[ V = A \times \text{length} \]
Given that the length of the canal is 120 meters:
\[ V = 9 \text{ m}^2 \times 120 \text{ m} \]
\[ V = 1080 \text{ m}^3 \]

5. **Conclusion**:
The maximum capacity of the canal is \( 1080 \text{ m}^3 \).