Deepali makes a model of a cylindrical kaleidoscope fo her science project. She uses a chart paper to make it. If the length of the kaleidoscope is 25 cm and radius 3.5 cm, the area of the paper she used, in square cm, is `(pi = (22)/(7))`

Options

A. 1100
B. 550
C. 500
D. 450

Answer

To find the area of the chart paper used to make the cylindrical kaleidoscope, we need to calculate the curved surface area (CSA) of the cylinder. The formula for the curved surface area of a cylinder is:

\[ \text{CSA} = 2 \pi r h \]

Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height (or length) of the cylinder,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) in this case.

### Step 1: Identify the values
- Radius \( r = 3.5 \) cm
- Height \( h = 25 \) cm
- \( \pi = \frac{22}{7} \)

### Step 2: Substitute the values into the formula
Using the formula for CSA:

\[ \text{CSA} = 2 \pi r h \]

Substituting the values we have:

\[ \text{CSA} = 2 \times \frac{22}{7} \times 3.5 \times 25 \]

### Step 3: Simplify the expression
First, calculate \( 2 \times \frac{22}{7} \):

\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

Now, we can substitute this back into the equation:

\[ \text{CSA} = \frac{44}{7} \times 3.5 \times 25 \]

Next, convert \( 3.5 \) to a fraction:

\[ 3.5 = \frac{35}{10} = \frac{7}{2} \]

Now, substitute \( 3.5 \):

\[ \text{CSA} = \frac{44}{7} \times \frac{7}{2} \times 25 \]

### Step 4: Cancel out the common terms
Notice that \( \frac{7}{7} \) cancels out:

\[ \text{CSA} = \frac{44}{2} \times 25 \]

### Step 5: Calculate \( \frac{44}{2} \)
\[ \frac{44}{2} = 22 \]

Now substitute this back into the equation:

\[ \text{CSA} = 22 \times 25 \]

### Step 6: Calculate the final area
Now, calculate \( 22 \times 25 \):

\[ 22 \times 25 = 550 \]

### Conclusion
The area of the paper used to make the cylindrical kaleidoscope is:

\[ \text{Area} = 550 \text{ cm}^2 \]