How many cubic metres of earth must be dug to make a well 14 m deep and 4m in diameter ?

Answer

To find out how many cubic meters of earth must be dug to make a well that is 14 meters deep and 4 meters in diameter, we can follow these steps:

### Step 1: Identify the dimensions of the well
- The depth (height) of the well is given as 14 meters.
- The diameter of the well is given as 4 meters.

### Step 2: Calculate the radius of the well
- The radius (R) is half of the diameter.
- Radius \( R = \frac{\text{Diameter}}{2} = \frac{4 \text{ m}}{2} = 2 \text{ m} \).

### Step 3: Use the formula for the volume of a cylinder
- The volume (V) of a cylinder is calculated using the formula:
\[ V = \pi R^2 H \]
where \( R \) is the radius and \( H \) is the height.

### Step 4: Substitute the values into the formula
- We know:
- \( \pi \approx \frac{22}{7} \) (for calculation purposes)
- \( R = 2 \text{ m} \)
- \( H = 14 \text{ m} \)

Substituting these values into the formula:
\[ V = \frac{22}{7} \times (2)^2 \times 14 \]

### Step 5: Calculate the volume
- First, calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
- Now substitute back into the volume formula:
\[ V = \frac{22}{7} \times 4 \times 14 \]
- Calculate \( 4 \times 14 = 56 \):
\[ V = \frac{22}{7} \times 56 \]
- Now multiply \( 22 \times 56 \):
\[ 22 \times 56 = 1232 \]
- Finally, divide by 7:
\[ V = \frac{1232}{7} \approx 176 \text{ m}^3 \]

### Conclusion
The volume of the well, which is the amount of earth that must be dug, is approximately **176 cubic meters**.

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