It is required to make a closed cylindrical tank of height 1m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ?

Answer

To find the amount of metal sheet required to make a closed cylindrical tank, we need to calculate the total surface area of the cylinder. The formula for the total surface area (TSA) of a closed cylinder is given by:

\[ \text{TSA} = 2\pi r(h + r) \]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.

### Step 1: Convert the dimensions to the same unit
The height of the cylinder is given as 1 meter, and the diameter is 140 cm. We need to convert the diameter to meters to match the height.

- Diameter = 140 cm = 1.4 m
- Radius \( r = \frac{\text{Diameter}}{2} = \frac{1.4 \, \text{m}}{2} = 0.7 \, \text{m} \)

### Step 2: Substitute the values into the TSA formula
Now we can substitute the values of \( r \) and \( h \) into the TSA formula.

- \( r = 0.7 \, \text{m} \)
- \( h = 1 \, \text{m} \)

\[ \text{TSA} = 2\pi(0.7)(1 + 0.7) \]

### Step 3: Simplify the expression
We can simplify the expression inside the parentheses:

\[ 1 + 0.7 = 1.7 \]

Now substituting this back into the TSA formula:

\[ \text{TSA} = 2\pi(0.7)(1.7) \]

### Step 4: Calculate the numerical value
Using \( \pi \approx \frac{22}{7} \):

\[ \text{TSA} = 2 \times \frac{22}{7} \times 0.7 \times 1.7 \]

Calculating \( 2 \times \frac{22}{7} \times 0.7 \):

\[ = \frac{44}{7} \times 0.7 = \frac{44 \times 0.7}{7} = \frac{30.8}{7} \]

Now, we multiply by 1.7:

\[ \text{TSA} = \frac{30.8}{7} \times 1.7 = \frac{30.8 \times 1.7}{7} = \frac{52.36}{7} \]

Calculating \( \frac{52.36}{7} \):

\[ \text{TSA} \approx 7.48 \, \text{m}^2 \]

### Final Answer
The total surface area of the cylindrical tank, and thus the area of the metal sheet required, is approximately:

\[ \text{TSA} \approx 7.48 \, \text{m}^2 \]