A closed cylindrical tank of diameter 14 m and height 5 m is made form a sheet of metal. How much sheet of metal will be required?

Answer

To find out how much sheet of metal will be required to make a closed cylindrical tank with a diameter of 14 m and a height of 5 m, we need to calculate the total surface area of the cylinder. Here’s the step-by-step solution:

### Step 1: Identify the dimensions of the cylinder
- **Diameter (d)** = 14 m
- **Height (h)** = 5 m

### Step 2: Calculate the radius of the cylinder
The radius (r) is half of the diameter.
\[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ m} \]

### Step 3: Use the formula for the total surface area of a closed cylinder
The total surface area (TSA) of a closed cylinder is given by the formula:
\[ \text{TSA} = 2\pi r(h + r) \]
Where:
- \( \pi \approx \frac{22}{7} \)
- \( r \) is the radius
- \( h \) is the height

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 7 \times (5 + 7) \]

### Step 5: Simplify the expression
First, calculate \( (5 + 7) \):
\[ 5 + 7 = 12 \]
Now substitute this back into the TSA formula:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 7 \times 12 \]

### Step 6: Calculate the TSA
The \( 7 \) in the numerator and denominator cancels out:
\[ \text{TSA} = 2 \times 22 \times 12 \]
Now calculate:
\[ 2 \times 22 = 44 \]
Then:
\[ 44 \times 12 = 528 \text{ m}^2 \]

### Conclusion
The total surface area, which is also the amount of sheet metal required, is:
\[ \text{Required sheet of metal} = 528 \text{ m}^2 \]

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