The diameter of a cylinder is 7 cm and its height is 16 cm. Using the value of `pi = (22)/(7)`, the lateral surface area of the cylinder is

Options

A. `352 cm^(2)`
B. `350 cm^(2)`
C. `355 cm^(2)`
D. `348 cm^(2)`

Answer

To find the lateral surface area of the 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
- Value of π = 22/7

### 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 lateral surface area
The formula for the lateral surface area (curved surface area) of a cylinder is:
\[ \text{Lateral Surface Area} = 2 \pi r h \]

### Step 4: Substitute the values into the formula
Now we substitute the values of π, r, and h into the formula:
\[ \text{Lateral Surface Area} = 2 \times \frac{22}{7} \times 3.5 \times 16 \]

### Step 5: Simplify the expression
First, we can simplify \(2 \times 3.5\):
\[ 2 \times 3.5 = 7 \]
Now substitute this back into the equation:
\[ \text{Lateral Surface Area} = \frac{22}{7} \times 7 \times 16 \]
The 7 in the numerator and denominator cancels out:
\[ \text{Lateral Surface Area} = 22 \times 16 \]

### Step 6: Calculate the final area
Now calculate \(22 \times 16\):
\[ 22 \times 16 = 352 \text{ cm}^2 \]

### Final Answer
The lateral surface area of the cylinder is \(352 \text{ cm}^2\).

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