A well, 2m radius and 40m deep, is being dug. The excavated soil is trasported using a truck of size `5mxx2mxxpim`. How many trips will the truck have to clear the excavated soil if it can be filled to 80% of its height?

Options

A. 10
B. 12
C. 20
D. 24

Answer

To solve the problem step by step, we will calculate the volume of the well, the volume of the truck that can be filled with excavated soil, and then determine how many trips the truck needs to make.

### Step 1: Calculate the volume of the well
The well is cylindrical in shape. The formula for the volume \( V \) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height (or depth) of the cylinder

Given:
- Radius \( r = 2 \) m
- Depth \( h = 40 \) m

Substituting the values into the formula:

\[ V = \pi (2^2)(40) = \pi (4)(40) = 160\pi \text{ cubic meters} \]

### Step 2: Calculate the volume of the truck
The truck is cuboidal in shape. The formula for the volume \( V \) of a cuboid is given by:

\[ V = l \times b \times h \]

Where:
- \( l \) is the length
- \( b \) is the breadth
- \( h \) is the height

Given:
- Length \( l = 5 \) m
- Breadth \( b = 2 \) m
- Height \( h = 5 \) m

Calculating the total volume of the truck:

\[ V = 5 \times 2 \times 5 = 50 \text{ cubic meters} \]

### Step 3: Calculate the effective volume of the truck for soil
The truck can only be filled to 80% of its height. Therefore, we need to calculate 80% of the truck's volume:

\[ \text{Effective Volume} = 50 \times \frac{80}{100} = 50 \times 0.8 = 40 \text{ cubic meters} \]

### Step 4: Calculate the number of trips required
To find the number of trips the truck needs to make, we divide the total volume of the well by the effective volume of the truck:

\[ \text{Number of trips} = \frac{\text{Volume of the well}}{\text{Effective Volume of the truck}} = \frac{160\pi}{40} \]

Calculating this gives:

\[ \text{Number of trips} = \frac{160\pi}{40} = 4\pi \]

Since \( \pi \) is approximately 3.14, we can calculate:

\[ 4\pi \approx 4 \times 3.14 = 12.56 \]

Since the number of trips must be a whole number, we round up to the nearest whole number, which is 13.

### Final Answer
The truck will need to make approximately **13 trips** to clear the excavated soil.

---