A right circular cylinder of height 16 cm is covered by a rectangular in the foil of size `16 cm xx 22 cm`. The volume of the cylinder is

Options

A. `352 cm^(3)`
B. `308 cm^(3)`
C. `616 cm^(3)`
D. `176 cm^(3)`

Answer

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

### Step 1: Identify the dimensions of the cylinder
The problem states that the height of the cylinder is 16 cm. The diameter of the cylinder corresponds to the smaller side of the rectangular foil, which is also 16 cm.

**Hint:** Remember that the diameter is twice the radius.

### Step 2: Calculate the radius of the cylinder
Since the diameter of the cylinder is 16 cm, we can find the radius by dividing the diameter by 2.

\[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{16 \, \text{cm}}{2} = 8 \, \text{cm} \]

**Hint:** The radius is half of the diameter.

### Step 3: Use the formula for the volume of a cylinder
The formula for the volume \( V \) of a right circular cylinder is given by:

\[ V = \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height.

**Hint:** Make sure to substitute the values correctly into the formula.

### Step 4: Substitute the values into the formula
Now we can substitute the radius and height into the volume formula. We will use \( \pi \approx \frac{22}{7} \) for our calculations.

\[ V = \pi r^2 h = \frac{22}{7} \times (8 \, \text{cm})^2 \times 16 \, \text{cm \]

Calculating \( (8 \, \text{cm})^2 \):

\[ (8 \, \text{cm})^2 = 64 \, \text{cm}^2 \]

Now substituting this back into the volume formula:

\[ V = \frac{22}{7} \times 64 \, \text{cm}^2 \times 16 \, \text{cm} \]

**Hint:** Ensure to multiply the area by the height to get the volume.

### Step 5: Perform the multiplication
Now we can calculate:

\[ V = \frac{22}{7} \times 64 \times 16 \]

Calculating \( 64 \times 16 \):

\[ 64 \times 16 = 1024 \]

Now substituting this back into the volume equation:

\[ V = \frac{22}{7} \times 1024 \]

**Hint:** When multiplying fractions, multiply the numerator and divide by the denominator.

### Step 6: Calculate the final volume
Now calculate:

\[ V = \frac{22 \times 1024}{7} = \frac{22488}{7} \approx 3212.57 \, \text{cm}^3 \]

**Hint:** Use a calculator for division if necessary.

### Final Answer
The volume of the cylinder is approximately \( 3212.57 \, \text{cm}^3 \).