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

Options

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

Answer

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

### Step 1: Understand the given dimensions
- The height (h) of the cylinder is given as 16 cm.
- The size of the rectangular tin foil is 16 cm x 22 cm.

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

### Step 3: Calculate the curved surface area using the dimensions of the foil
The area of the rectangular tin foil is:
\[ \text{Area} = 16 \, \text{cm} \times 22 \, \text{cm} = 352 \, \text{cm}^2 \]

Since the curved surface area of the cylinder is equal to the area of the rectangular foil:
\[ 2\pi rh = 352 \]

### Step 4: Substitute the height and solve for the radius
Substituting \( h = 16 \, \text{cm} \) into the equation:
\[ 2\pi r(16) = 352 \]
\[ 32\pi r = 352 \]
Now, divide both sides by \( 32\pi \):
\[ r = \frac{352}{32\pi} \]

### Step 5: Simplify the radius
Calculating \( \frac{352}{32} \):
\[ \frac{352}{32} = 11 \]
So,
\[ r = \frac{11}{\pi} \]

### Step 6: Calculate the volume of the cylinder
The volume \( V \) of the cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting \( r = \frac{11}{\pi} \) and \( h = 16 \):
\[ V = \pi \left(\frac{11}{\pi}\right)^2 (16) \]
\[ V = \pi \left(\frac{121}{\pi^2}\right) (16) \]
\[ V = \frac{121 \times 16}{\pi} \]

### Step 7: Calculate the final volume
Now, we can calculate:
\[ V = \frac{1936}{\pi} \]
Using \( \pi \approx 3.14 \):
\[ V \approx \frac{1936}{3.14} \approx 617.72 \, \text{cm}^3 \]

### Step 8: Round to the nearest whole number
Thus, the volume of the cylinder is approximately:
\[ V \approx 616 \, \text{cm}^3 \]

### Final Answer
The volume of the cylinder is **616 cm³**.

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