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

Answer

To find the volume of a right circular cylinder, we can follow these steps:

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

### Step 2: Substitute the given circumference
We know that the circumference of the base of the cylinder is 528 cm. Therefore, we can set up the equation:
\[ 2\pi r = 528 \]

### Step 3: Solve for the radius (r)
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r = 528 \]

Now, simplify:
\[ \frac{44}{7} r = 528 \]

To find \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 528 \times \frac{7}{44} \]

Calculating this gives:
\[ r = 528 \div 44 \times 7 \]
\[ r = 12 \times 7 \]
\[ r = 84 \text{ cm} \]

### Step 4: Convert radius to meters
Since the height is given in meters, we should convert the radius from centimeters to meters:
\[ r = \frac{84 \text{ cm}}{100} = 0.84 \text{ m} \]

### Step 5: Use the volume formula for the cylinder
The volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( h \) is the height of the cylinder.

### Step 6: Substitute the values into the volume formula
We know:
- \( r = 0.84 \text{ m} \)
- \( h = 2 \text{ m} \)
- \( \pi = \frac{22}{7} \)

Now substitute these values into the volume formula:
\[ V = \frac{22}{7} \times (0.84)^2 \times 2 \]

### Step 7: Calculate \( (0.84)^2 \)
Calculating \( (0.84)^2 \):
\[ (0.84)^2 = 0.7056 \]

### Step 8: Substitute back into the volume formula
Now substitute this back into the volume formula:
\[ V = \frac{22}{7} \times 0.7056 \times 2 \]

### Step 9: Calculate the volume
First, calculate \( 0.7056 \times 2 = 1.4112 \).
Now substitute:
\[ V = \frac{22}{7} \times 1.4112 \]

Calculating this gives:
\[ V = \frac{22 \times 1.4112}{7} \]
\[ V = \frac{31.0464}{7} \]
\[ V = 4.4323 \text{ m}^3 \]

### Step 10: Round the answer
The final volume of the cylinder is approximately:
\[ V \approx 4.4352 \text{ m}^3 \]

### Final Answer:
The volume of the cylinder is **4.4352 m³**.