A rectangular paper is 44\text{ cm} long and 22\text{ cm} wide. Let x be the volume of the largest cylinder formed by rolling the paper along its length and y be the volume of the largest cylinder formed by rolling the paper along its width. What is the ratio of x to y? (Take \pi=\frac{22}{7})
- A. 1:1
- B. 2:1 ✓
- C. 1:2
- D. 3:2
Correct Answer: B. 2:1
Explanation
Rolled along length: circumference 2\pi r_1 = 44 \implies r_1 = 7, height h_1 = 22. Volume x = \pi(7^2)(22) = 1078\pi. Rolled along width: circumference 2\pi r_2 = 22 \implies r_2 = 3.5, height h_2 = 44. Volume y = \pi(3.5^2)(44) = 539\pi. Ratio x:y = 1078\pi : 539\pi = 2:1.
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