The diamter of a closed cylinder is 7 cm and its heght is 16 cm. Find:
the total surface area of the cylinder.

Answer

To find the total surface area of a closed cylinder, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the cylinder (d) = 7 cm
- Height of the cylinder (h) = 16 cm

### Step 2: Calculate the radius of the cylinder
The radius (r) is half of the diameter.
\[ r = \frac{d}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

### Step 3: Use the formula for the total surface area of a closed cylinder
The formula for the total surface area (TSA) of a closed cylinder is:
\[ \text{TSA} = 2\pi r(h + r) \]
Where:
- \( \pi \) is approximately \( \frac{22}{7} \) or \( 3.14 \)

### Step 4: Substitute the values into the formula
Substituting \( r = 3.5 \) cm and \( h = 16 \) cm into the formula:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 3.5 \times (16 + 3.5) \]

### Step 5: Calculate \( (16 + 3.5) \)
\[ 16 + 3.5 = 19.5 \]

### Step 6: Substitute back into the TSA formula
\[ \text{TSA} = 2 \times \frac{22}{7} \times 3.5 \times 19.5 \]

### Step 7: Simplify the expression
First, calculate \( 2 \times 3.5 = 7 \):
\[ \text{TSA} = \frac{22}{7} \times 7 \times 19.5 \]
The \( 7 \) in the numerator and denominator cancels out:
\[ \text{TSA} = 22 \times 19.5 \]

### Step 8: Calculate \( 22 \times 19.5 \)
\[ 22 \times 19.5 = 429 \]

### Step 9: Finalize the total surface area
Thus, the total surface area of the cylinder is:
\[ \text{TSA} = 429 \text{ cm}^2 \]

### Summary
The total surface area of the closed cylinder is \( 429 \text{ cm}^2 \).

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