A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

Answer

To solve the problem of finding the depth of the circular tank, we will follow these steps:

### Step 1: Understand the dimensions
- The diameter of the circular tank is given as 2 m.
- Therefore, the radius (r) of the tank is:
\[ r = \frac{diameter}{2} = \frac{2}{2} = 1 \text{ m} \]
- The embankment around the tank has a width of 2 m and a height of 1.6 m.

### Step 2: Determine the outer radius of the embankment
- The outer radius (R) of the embankment can be calculated as:
\[ R = r + \text{width of embankment} = 1 + 2 = 3 \text{ m} \]

### Step 3: Calculate the volume of the earth removed
- The volume of the earth removed from the tank is equal to the volume of the tank itself, which is cylindrical in shape:
\[ \text{Volume of the tank} = \pi r^2 h \]
where \( h \) is the depth we need to find.

### Step 4: Calculate the volume of the embankment
- The volume of the embankment can be calculated using the area of the ring (the difference between the outer and inner circles) multiplied by the height of the embankment:
\[ \text{Volume of the embankment} = \text{Area of the ring} \times \text{height} \]
\[ = \pi (R^2 - r^2) \times \text{height} \]
\[ = \pi (3^2 - 1^2) \times 1.6 \]
\[ = \pi (9 - 1) \times 1.6 = \pi \times 8 \times 1.6 \]

### Step 5: Set the volumes equal to each other
- Since the volume of earth removed is equal to the volume of the embankment:
\[ \pi r^2 h = \pi (8 \times 1.6) \]
- We can cancel \( \pi \) from both sides:
\[ r^2 h = 8 \times 1.6 \]

### Step 6: Substitute the value of \( r \)
- Substitute \( r = 1 \):
\[ (1^2) h = 8 \times 1.6 \]
\[ h = 8 \times 1.6 = 12.8 \text{ m} \]

### Final Answer
- Therefore, the depth of the circular tank is:
\[ \text{Depth} = 12.8 \text{ m} \]