The circumference of the base of a cylinder vessel is 132 cm and height is 25 cm. Find the volume of cylinder.
(use `pi=22/(7)`)

Options

A. `34650 cm^3`
B. `35650 cm^3`
C. `3460 cm^3`
D. None

Explanation

To find the volume of a cylinder given the circumference of its base and its height, we can follow these steps:

### Step 1: Understand the relationship between circumference and radius
The circumference \( C \) of a cylinder is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius and \( \pi \) is a constant approximately equal to \( \frac{22}{7} \).

### Step 2: Substitute the given circumference into the formula
We know that the circumference is 132 cm, so we can set up the equation:
\[ 2\pi r = 132 \]

### Step 3: Substitute the value of \( \pi \)
Using \( \pi = \frac{22}{7} \), we can rewrite the equation:
\[ 2 \times \frac{22}{7} \times r = 132 \]

### Step 4: Simplify the equation to solve for \( r \)
Multiplying both sides by 7 to eliminate the fraction:
\[ 2 \times 22 \times r = 132 \times 7 \]
\[ 44r = 924 \]

### Step 5: Solve for \( r \)
Now, divide both sides by 44:
\[ r = \frac{924}{44} \]
\[ r = 21 \text{ cm} \]

### Step 6: Use the radius to find the volume of the cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( h \) is the height of the cylinder.

### Step 7: Substitute the values of \( r \) and \( h \)
Given that the height \( h = 25 \) cm, we substitute \( r = 21 \) cm into the volume formula:
\[ V = \frac{22}{7} \times (21)^2 \times 25 \]

### Step 8: Calculate \( (21)^2 \)
Calculating \( (21)^2 \):
\[ (21)^2 = 441 \]

### Step 9: Substitute back into the volume formula
Now substitute \( 441 \) into the volume formula:
\[ V = \frac{22}{7} \times 441 \times 25 \]

### Step 10: Simplify the expression
First, calculate \( \frac{22 \times 441}{7} \):
\[ \frac{22 \times 441}{7} = 22 \times 63 = 1386 \]
Now multiply by 25:
\[ V = 1386 \times 25 \]

### Step 11: Calculate the final volume
Calculating \( 1386 \times 25 \):
\[ V = 34650 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder is:
\[ \boxed{34650 \text{ cm}^3} \]