A cylindrical well of depth 20 metres and radius 14 metres is dug in a field 72 metres long 44 metres wide. The earth taken out is spread evenly on the field. What is the increase (in metre) in the level of the field ?

Options

A. `6.67`
B. `3.56`
C. `5.61`
D. `4.83`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the volume of the cylindrical well.
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 in this case) of the cylinder.

Given:
- Radius \( r = 14 \) meters,
- Depth \( h = 20 \) meters.

Substituting the values into the formula:

\[ V = \pi \times (14)^2 \times 20 \]

Calculating \( (14)^2 \):

\[ (14)^2 = 196 \]

Now substituting back into the volume formula:

\[ V = \pi \times 196 \times 20 \]

Using \( \pi \approx \frac{22}{7} \):

\[ V \approx \frac{22}{7} \times 196 \times 20 \]

Calculating \( 196 \times 20 \):

\[ 196 \times 20 = 3920 \]

Now substituting back:

\[ V \approx \frac{22}{7} \times 3920 \]

Calculating \( \frac{22 \times 3920}{7} \):

\[ \frac{22 \times 3920}{7} = \frac{86240}{7} \approx 12320 \text{ cubic meters} \]

### Step 2: Calculate the area of the field.
The area \( A \) of the rectangular field is given by:

\[ A = \text{length} \times \text{width} \]

Given:
- Length = 72 meters,
- Width = 44 meters.

Calculating the area:

\[ A = 72 \times 44 = 3168 \text{ square meters} \]

### Step 3: Calculate the increase in the level of the field.
The volume of the earth taken out from the well is spread evenly over the area of the field. Let \( h \) be the increase in the level of the field.

The volume of the earth spread over the field can also be expressed as:

\[ \text{Volume} = \text{Area} \times \text{Height} \]

Thus, we have:

\[ 12320 = 3168 \times h \]

To find \( h \), we rearrange the equation:

\[ h = \frac{12320}{3168} \]

Calculating \( h \):

\[ h \approx 3.89 \text{ meters} \]

### Final Answer:
The increase in the level of the field is approximately **3.89 meters**.

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