A rectangular tin sheet is 22 m long and 8 m broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other . The volume of the cylinder ( in `m^(3) `) is :

Options

A. `385`
B. `204`
C. `280 pi`
D. 308

Answer

To find the volume of the cylinder formed by rolling a rectangular tin sheet, we can follow these steps:

### Step 1: Identify the dimensions of the rectangular sheet
The dimensions given are:
- Length (L) = 22 m
- Breadth (B) = 8 m

### Step 2: Understand how the sheet is rolled
When the rectangular sheet is rolled along its length, the length of the sheet becomes the circumference of the base of the cylinder, and the breadth of the sheet becomes the height of the cylinder.

### Step 3: Set the height and circumference
- Height (h) of the cylinder = Breadth of the sheet = 8 m
- Circumference (C) of the cylinder = Length of the sheet = 22 m

### Step 4: Relate circumference to radius
The circumference of a cylinder is given by the formula:
\[ C = 2\pi r \]
Where \( r \) is the radius of the base of the cylinder.

From the circumference:
\[ 2\pi r = 22 \]

### Step 5: Solve for the radius
To find the radius \( r \):
\[ r = \frac{22}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{22}{2 \times \frac{22}{7}} \]
\[ r = \frac{22 \times 7}{44} \]
\[ r = \frac{7}{2} \text{ m} \]

### Step 6: Calculate the volume of the cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting the values we have:
- \( r = \frac{7}{2} \)
- \( h = 8 \)

Calculating \( V \):
\[ V = \pi \left(\frac{7}{2}\right)^2 \times 8 \]
\[ V = \pi \times \frac{49}{4} \times 8 \]
\[ V = \pi \times \frac{49 \times 8}{4} \]
\[ V = \pi \times 98 \]
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 98 \]
\[ V = \frac{22 \times 98}{7} \]
\[ V = 22 \times 14 \]
\[ V = 308 \text{ m}^3 \]

### Final Answer
The volume of the cylinder is **308 m³**.

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