The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find :
the total surface area.

Answer

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

### Step 1: Identify the given values
- Height (h) of the cylinder = 20 cm
- Radius (r) of the base = 7 cm

### Step 2: Write the formula for the total surface area (TSA) of a cylinder
The total surface area of a cylinder is given by the formula:
\[ \text{TSA} = \text{Curved Surface Area} + \text{Area of two circular bases} \]
Where:
- Curved Surface Area (CSA) = \(2\pi rh\)
- Area of two circular bases = \(2\pi r^2\)

### Step 3: Substitute the values into the formula
Using \(\pi \approx \frac{22}{7}\):
1. Calculate the Curved Surface Area (CSA):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 7 \times 20 \]
2. Calculate the Area of two circular bases:
\[ \text{Area of two bases} = 2 \times \frac{22}{7} \times 7^2 \]

### Step 4: Calculate the Curved Surface Area (CSA)
1. Simplifying the CSA:
\[ \text{CSA} = 2 \times \frac{22}{7} \times 7 \times 20 = 2 \times 22 \times 20 \]
\[ = 44 \times 20 = 880 \text{ cm}^2 \]

### Step 5: Calculate the Area of two circular bases
1. Simplifying the area of two bases:
\[ \text{Area of two bases} = 2 \times \frac{22}{7} \times 7^2 = 2 \times \frac{22}{7} \times 49 \]
\[ = 2 \times 22 \times 7 = 308 \text{ cm}^2 \]

### Step 6: Add the two areas to find the Total Surface Area
\[ \text{TSA} = \text{CSA} + \text{Area of two bases} = 880 + 308 = 1188 \text{ cm}^2 \]

### Final Answer
The total surface area of the cylinder is \(1188 \text{ cm}^2\).

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