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Cylinder with a given ratio of curved to total surface area

This type of question, asked 3 times: CDS 2 2016, CDS 2 2018, CDS 1 2023. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    43
    The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm2616\ \text{cm}^2, what is the volume of the cylinder ?

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  2. Question 2

    CDS 2 2018

    79
    A solid right cylinder is of height π\pi cm. If its lateral surface area is half its total surface area, then the radius of its base is

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  3. Question 3

    CDS 1 2023

    62
    Two times the total surface area of a solid right circular cylinder is three times its curved surface area. If h is the height and r is the radius of the base of the cylinder, then which one of the following is correct ?

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