The height of a cylinder is 14 cm and its curved surface area is `264 cm^(2)`. The volume of the cylinder is

Options

A. `308 cm^(3)`
B. `396 cm^(3)`
C. `1232 cm^(3)`
D. `1848 cm^(3)`

Explanation

To find the volume of the cylinder, we will follow these steps:

### Step 1: Understand the given information
We know:
- Height (H) of the cylinder = 14 cm
- Curved Surface Area (CSA) of the cylinder = 264 cm²

### Step 2: Use the formula for Curved Surface Area of a Cylinder
The formula for the curved surface area of a cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 264 = 2 \times \frac{22}{7} \times r \times 14 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 264 = 2 \times \frac{22}{7} \times r \times 14 \]
\[ 264 = \frac{44}{7} \times r \times 14 \]
\[ 264 = \frac{616}{7} \times r \]

### Step 5: Solve for the radius (r)
To isolate \( r \), multiply both sides by \( 7 \):
\[ 264 \times 7 = 616 r \]
\[ 1848 = 616 r \]
Now, divide both sides by 616:
\[ r = \frac{1848}{616} \]
\[ r = 3 \text{ cm} \]

### Step 6: Use the radius to find the volume
Now that we have the radius, we can find the volume of the cylinder using the formula:
\[ \text{Volume} = \pi r^2 h \]

### Step 7: Substitute the values into the volume formula
Substituting the values we have:
\[ \text{Volume} = \frac{22}{7} \times (3)^2 \times 14 \]
\[ \text{Volume} = \frac{22}{7} \times 9 \times 14 \]

### Step 8: Calculate the volume
Now, calculate:
\[ \text{Volume} = \frac{22 \times 9 \times 14}{7} \]
\[ \text{Volume} = \frac{2772}{7} \]
\[ \text{Volume} = 396 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder is **396 cm³**.

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