Find the curved surface area (in `"cm"^2`) of a right circular cylinder of diameter 42 cm and height 14 cm.

Options

A. 1848
B. 1716
C. 1621
D. 1587

Answer

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

### Step 1: Identify the given values
- Diameter of the cylinder (d) = 42 cm
- Height of the cylinder (h) = 14 cm

### Step 2: Calculate the radius of the cylinder
The radius (r) is half of the diameter.
\[ r = \frac{d}{2} = \frac{42 \, \text{cm}}{2} = 21 \, \text{cm} \]

### Step 3: Use the formula for the curved surface area of a cylinder
The formula for the curved surface area (CSA) of a right circular cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]

### Step 4: Substitute the values into the formula
Using \(\pi \approx \frac{22}{7}\), we can substitute the values of \(r\) and \(h\):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 21 \, \text{cm} \times 14 \, \text{cm} \]

### Step 5: Simplify the expression
First, calculate \(2 \times \frac{22}{7}\):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

Now substitute this back into the equation:
\[ \text{CSA} = \frac{44}{7} \times 21 \times 14 \]

Next, simplify \(21 \times 14\):
\[ 21 \times 14 = 294 \]

Now substitute this value:
\[ \text{CSA} = \frac{44}{7} \times 294 \]

### Step 6: Calculate the final value
Now, divide 294 by 7:
\[ 294 \div 7 = 42 \]
Then multiply by 44:
\[ \text{CSA} = 44 \times 42 = 1848 \, \text{cm}^2 \]

### Final Answer
The curved surface area of the cylinder is \(1848 \, \text{cm}^2\).

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