Question

A rectangular sheet of paper 40 cm \( \times \) 22 cm is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder will be:

• A. 3.5 cm
• B. 7 cm
• C. \( \frac{80}{7} \) cm
• D. None of these

Hint:

The radius of a cylinder formed by rolling a rectangular sheet is given by \( r = \frac{\text{Length of the rectangle}}{2\pi} \).

Answer 1

The Correct Option is B

When the rectangular sheet is rolled to form a hollow cylinder, the height of the cylinder is the same as the height of the rectangle, which is 40 cm. The circumference of the base of the cylinder is equal to the length of the rectangle, which is 22 cm: \[ \text{Circumference} = 2\pi r = 22 \Rightarrow r = \frac{22}{2\pi} = \frac{11}{\pi} \approx 7 \, \text{cm}. \]
Step 2: Conclusion.
Therefore, the radius of the cylinder is 7 cm. So, the correct answer is (B).