A rectangular sheet of paper which is 88 cm long and 11 cm wide is rolled to form a cylinder of height equal to its width of the paper. What is the volume of the cylinder so formed?

Options

A. `7676cm^(3)`
B. `6776cm^(3)`
C. `6546cm^(3)`
D. `6786cm^(3)`

Answer

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

### Step 1: Identify the dimensions of the rectangular sheet
The dimensions of the rectangular sheet are given as:
- Length (L) = 88 cm
- Width (W) = 11 cm

### Step 2: Understand the formation of the cylinder
When the rectangular sheet is rolled to form a cylinder, the height (h) of the cylinder will be equal to the width of the paper:
- Height (h) = Width (W) = 11 cm

The length of the paper will become the circumference (C) of the base of the cylinder:
- Circumference (C) = Length (L) = 88 cm

### Step 3: Relate circumference to the radius
The formula for the circumference of a circle is given by:
\[ C = 2\pi r \]
Where \( r \) is the radius of the base of the cylinder. We can rearrange this formula to find the radius:
\[ r = \frac{C}{2\pi} \]

### Step 4: Substitute the known values
Substituting the circumference into the formula:
\[ r = \frac{88}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{88}{2 \times \frac{22}{7}} \]
\[ r = \frac{88 \times 7}{44} \]
\[ r = \frac{616}{44} \]
\[ r = 14 \text{ cm} \]

### Step 5: 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 of \( r \) and \( h \):
\[ V = \pi \times (14)^2 \times 11 \]
\[ V = \pi \times 196 \times 11 \]
\[ V = \pi \times 2156 \]

Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 2156 \]

### Step 6: Simplify the volume calculation
\[ V = \frac{22 \times 2156}{7} \]
Calculating \( 22 \times 2156 = 47432 \):
\[ V = \frac{47432}{7} \]
Calculating \( \frac{47432}{7} = 6760 \text{ cm}^3 \)

Thus, the volume of the cylinder is:
\[ V = 6760 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder formed is **6760 cm³**.

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