The circumference of the base of a right circular cylinder is 528 cm and its height is 2 m. What is the volume of the cylinder?
(Take `pi = (22)/(7)`)

Options

A. `6.6528 m^(3)`
B. `2.2176 m^(3)`
C. `3.3264 m^(3)`
D. `4.4352 m^(3)`

Answer

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

### Step 1: Understand the formula for circumference
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

### Step 2: Rearrange the formula to find the radius
We can rearrange the formula to solve for \( r \):
\[ r = \frac{C}{2 \pi} \]

### Step 3: Substitute the given values
We know the circumference \( C = 528 \) cm and we will use \( \pi = \frac{22}{7} \):
\[ r = \frac{528}{2 \times \frac{22}{7}} = \frac{528 \times 7}{44} \]

### Step 4: Calculate the radius
Now, we simplify the calculation:
\[ r = \frac{528 \times 7}{44} = \frac{3696}{44} = 84 \text{ cm} \]

### Step 5: Convert the radius to meters
Since the height is given in meters, we should convert the radius from centimeters to meters:
\[ r = \frac{84}{100} = 0.84 \text{ m} \]

### Step 6: Use the formula for the volume of a 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 into the volume formula
Given \( h = 2 \) m, we substitute the values:
\[ V = \frac{22}{7} \times (0.84)^2 \times 2 \]

### Step 8: Calculate \( r^2 \)
First, calculate \( (0.84)^2 \):
\[ (0.84)^2 = 0.7056 \]

### Step 9: Calculate the volume
Now substitute \( r^2 \) back into the volume formula:
\[ V = \frac{22}{7} \times 0.7056 \times 2 \]
\[ V = \frac{22 \times 0.7056 \times 2}{7} \]
\[ V = \frac{31.0976}{7} \approx 4.43 \text{ m}^3 \]

### Step 10: Final volume in cubic centimeters
To convert the volume from cubic meters to cubic centimeters, we multiply by \( 1,000,000 \):
\[ V \approx 4.43 \times 1,000,000 \approx 4430000 \text{ cm}^3 \]

### Conclusion
The volume of the cylinder is approximately \( 4430000 \text{ cm}^3 \).

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