Find the total surface area of the cylinder, if the radius of its base is 5 cm and height is 40 cm. (`pi`= 3.14)

Explanation

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

### Step 1: Understand the formula for total surface area of a cylinder
The total surface area (TSA) of a cylinder is given by the formula:
\[ \text{TSA} = 2\pi rh + 2\pi r^2 \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14.

### Step 2: Identify the given values
From the question, we have:
- Radius \( r = 5 \) cm
- Height \( h = 40 \) cm
- \( \pi = 3.14 \)

### Step 3: Substitute the values into the formula
Now we substitute the values into the TSA formula:
\[ \text{TSA} = 2 \times 3.14 \times 5 \times 40 + 2 \times 3.14 \times 5^2 \]

### Step 4: Calculate the curved surface area
First, calculate the curved surface area:
\[ \text{Curved Surface Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 40 \]
Calculating this step by step:
\[ = 2 \times 3.14 = 6.28 \]
\[ 6.28 \times 5 = 31.4 \]
\[ 31.4 \times 40 = 1256 \text{ cm}^2 \]

### Step 5: Calculate the area of the two circular bases
Now calculate the area of the two circular bases:
\[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times 5^2 \]
Calculating this step by step:
\[ = 2 \times 3.14 \times 25 \]
\[ = 2 \times 3.14 = 6.28 \]
\[ 6.28 \times 25 = 157 \text{ cm}^2 \]

### Step 6: Add both areas to find the total surface area
Now, we add the curved surface area and the area of the bases:
\[ \text{TSA} = 1256 + 157 = 1413 \text{ cm}^2 \]

### Final Answer
The total surface area of the cylinder is:
\[ \text{TSA} = 1413 \text{ cm}^2 \]

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