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Cube and sphere with equal surface areas: compare sides, radii or volumes

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

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  1. Question 1

    CDS 1 2021

    80
    The surface area of a cube is equal to that of a sphere. If xx is the volume of the cube and yy is the volume of the sphere, then what is x2:y2x^2 : y^2 equal to?

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  2. Question 2

    CDS 1 2022

    63
    The surface area of a cube of length xx is equal to the surface area of a sphere of radius yy. Consider the following statements : 1. 2x>3y2x > 3y 2. The volume of the cube is greater than the volume of the sphere. Which of the above statements is/are correct?

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