The radius of the base of cylinder is 14 cm and its curved surface area is `880 cm^2`. Its volume (in `cm^3)` is :
(Take `pi = 22/7)`

Options

A. 3080
B. 6160
C. 1078
D. 9240

Answer

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

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

### Step 2: Substitute the known values into the CSA formula.
Given:
- Radius \( r = 14 \) cm
- Curved Surface Area \( \text{CSA} = 880 \) cm²

Substituting these values into the formula:
\[ 880 = 2 \times \frac{22}{7} \times 14 \times h \]

### Step 3: Simplify the equation to find the height \( h \).
First, calculate \( 2 \times \frac{22}{7} \times 14 \):
\[ 2 \times \frac{22}{7} \times 14 = \frac{2 \times 22 \times 14}{7} = \frac{616}{7} \]
Now, substituting back into the equation:
\[ 880 = \frac{616}{7} \times h \]
To isolate \( h \), multiply both sides by \( \frac{7}{616} \):
\[ h = 880 \times \frac{7}{616} \]

### Step 4: Calculate the height \( h \).
First, simplify \( \frac{880 \times 7}{616} \):
\[ h = \frac{6160}{616} = 10 \text{ cm} \]

### Step 5: Use the height to find the volume of the cylinder.
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
Substituting the known values:
\[ V = \frac{22}{7} \times (14)^2 \times 10 \]
Calculating \( (14)^2 = 196 \):
\[ V = \frac{22}{7} \times 196 \times 10 \]

### Step 6: Calculate the volume.
First, calculate \( \frac{22 \times 196}{7} \):
\[ \frac{22 \times 196}{7} = \frac{4312}{7} = 616 \]
Now, multiply by 10:
\[ V = 616 \times 10 = 6160 \text{ cm}^3 \]

### Final Answer:
The volume of the cylinder is \( 6160 \text{ cm}^3 \).

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