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Rectangular sheet rolled into a cylinder: volume

This type of question, asked 4 times: CDS 2 2017, CDS 1 2021, CDS 1 2022, CDS 1 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    76
    Two rectangular sheets of sizes 2π×4π2\pi \times 4\pi and π×5π\pi \times 5\pi are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheet. What is the maximum possible volume of the circular cylinder that can be formed this way ?

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  2. Question 2

    CDS 1 2021

    69
    A rectangular paper is 44 cm long and 22 cm wide. Let xx be the volume of the largest cylinder formed by rolling the paper along its length and yy be the volume of the largest cylinder formed by rolling the paper along its width. What is the ratio of xx to yy? (Take π=227\pi = \frac{22}{7})

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  3. Question 3

    CDS 1 2022

    69
    A rectangular sheet is of length xx and breadth yy. If pp is the volume of the cylinder formed by rolling the sheet along its breadth and qq is the volume of the cylinder formed by rolling the sheet along its length, and q=2pq = 2p, then which one of the following is correct?

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  4. Question 4

    CDS 1 2023

    86
    A square sheet of side length 44 cm is rolled along one of its sides to form a cylinder by making opposite edges just to touch each other. What is the volume of the cylinder ? (Take π=227\pi = \frac{22}{7})

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