What is the total surface area of cylinder of radius 25 cm and height of 0.8m?

Options

A. `1.54m^(2)`
B. `1.77 m ^(2)`
C. `1.65 m ^(2)`
D. `1.80 m ^(2)`

Answer

To find the total surface area of a cylinder, we can use the formula:

\[ \text{Total Surface Area} = 2\pi r (r + h) \]

where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 1: Convert Units
The radius is given in centimeters and the height in meters. We need to convert the radius from centimeters to meters.

- Radius \( r = 25 \) cm
- Convert to meters:
\[ r = \frac{25}{100} = 0.25 \text{ m} \]

### Step 2: Identify the Height
The height is already given in meters.

- Height \( h = 0.8 \) m

### Step 3: Substitute Values into the Formula
Now we can substitute the values of \( r \) and \( h \) into the total surface area formula.

\[ \text{Total Surface Area} = 2\pi (0.25) (0.25 + 0.8) \]

### Step 4: Calculate \( r + h \)
Calculate \( r + h \):

\[ 0.25 + 0.8 = 1.05 \]

### Step 5: Substitute and Calculate
Now substitute back into the formula:

\[ \text{Total Surface Area} = 2 \times \frac{22}{7} \times 0.25 \times 1.05 \]

### Step 6: Calculate the Multiplication
Calculate the multiplication step by step:

1. Calculate \( 2 \times \frac{22}{7} = \frac{44}{7} \)
2. Now multiply by \( 0.25 \):
\[ \frac{44}{7} \times 0.25 = \frac{44 \times 0.25}{7} = \frac{11}{7} \]
3. Finally, multiply by \( 1.05 \):
\[ \frac{11}{7} \times 1.05 = \frac{11 \times 1.05}{7} = \frac{11.55}{7} \approx 1.65 \]

### Final Answer
Thus, the total surface area of the cylinder is approximately:

\[ \text{Total Surface Area} \approx 1.65 \text{ m}^2 \]