Find the total surface area (in `cm^(2)`) of a right circular cylinder of diameter 28 cm., and height 12 cm.

Options

A. a.2200
B. b.2080
C. c.1920
D. d.2288

Answer

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

### Step 1: Identify the given values
- Diameter of the cylinder (d) = 28 cm
- Height of the cylinder (h) = 12 cm

### Step 2: Calculate the radius
The radius (r) is half of the diameter.
\[ r = \frac{d}{2} = \frac{28 \, \text{cm}}{2} = 14 \, \text{cm} \]

### Step 3: Write the formula for total surface area
The formula for the total surface area (TSA) of a right circular cylinder is:
\[ \text{TSA} = 2\pi r (r + h) \]

### Step 4: Substitute the values into the formula
Using \(\pi \approx \frac{22}{7}\):
\[ \text{TSA} = 2 \times \frac{22}{7} \times 14 \times (14 + 12) \]
\[ = 2 \times \frac{22}{7} \times 14 \times 26 \]

### Step 5: Simplify the expression
First, simplify \(2 \times 14\):
\[ = \frac{22}{7} \times 28 \times 26 \]

Now, calculate \(28 \div 7\):
\[ = 4 \times 22 \times 26 \]

### Step 6: Calculate the product
Now multiply:
\[ = 4 \times 22 = 88 \]
\[ = 88 \times 26 \]

Calculating \(88 \times 26\):
\[ = 88 \times 26 = 2288 \]

### Step 7: Write the final answer
Thus, the total surface area of the cylinder is:
\[ \text{TSA} = 2288 \, \text{cm}^2 \]

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