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 can follow these steps:

### Step 1: Understand the formulas
The curved surface area (CSA) of a cylinder is given by the formula:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values
We know the height \( h = 14 \) cm and the curved surface area \( \text{CSA} = 264 \) cm². We can substitute these values into the CSA formula:
\[ 264 = 2 \pi r \times 14 \]

### Step 3: Simplify the equation
Now, we simplify the equation to find \( r \):
\[ 264 = 28 \pi r \]
Dividing both sides by \( 28 \pi \):
\[ r = \frac{264}{28 \pi} \]

### Step 4: Calculate \( r \)
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{264}{28 \times \frac{22}{7}} = \frac{264 \times 7}{28 \times 22} \]
Now simplify:
\[ r = \frac{1848}{616} \]
Reducing this fraction:
\[ r = 3 \text{ cm} \]

### Step 5: Calculate the volume of the cylinder
The volume \( V \) of the cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting the values of \( r \) and \( h \):
\[ V = \pi \times (3)^2 \times 14 \]
Calculating further:
\[ V = \pi \times 9 \times 14 = 126 \pi \]
Using \( \pi \approx \frac{22}{7} \):
\[ V = 126 \times \frac{22}{7} = 396 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder is:
\[ \boxed{396 \text{ cm}^3} \]

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