Question

If a square shaped iron sheet is folded to form a cylinder, then what will be the ratio between the diameter of the cylinder thus formed and the side of the square iron sheet?

• A. \(\frac{1}{\pi}\)
• B. \(\frac{1}{2\pi}\)
• C. \(\frac{\sqrt2}{\pi}\)
• D. \(\frac{1}{\sqrt(2\pi)}\)

Answer 1

The Correct Option is B

Finding the Ratio Between the Diameter of the Cylinder and the Side of the Square 

Step 1: Define the Side Length of the Square

Let the side length of the square iron sheet be \( s \).

Step 2: Relationship Between the Square and the Cylinder

When the sheet is rolled into a cylinder, the circumference of the base of the cylinder equals the side of the square:

\[ \text{Circumference} = s \]

Step 3: Use the Formula for the Circumference of a Cylinder

The circumference of a cylinder is given by:

\[ 2\pi r = s \]

Solving for the diameter \( D \):

\[ D = 2r = \frac{s}{\pi} \]

Step 4: Compute the Required Ratio

The ratio between the diameter and the side of the square is:

\[ \frac{D}{s} = \frac{\frac{s}{\pi}}{s} = \frac{1}{\pi} \]

Final Answer:

Thus, the correct answer is \( \frac{1}{\pi} \) (Option B).