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8 January, 05:19

The ratio of the volumes of two similar circular cylinders is 27:64. What is the ratio of the

diameters of their similar bases?

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Answers (1)
  1. 8 January, 08:04
    0
    The ratio of their bases = 3√3 : 8

    Step-by-step explanation:

    Given,

    The ratio of the volume of two cylinders is 27:64.

    To find the ratio of the diameters of the cylinders of their base.

    Formula

    Let, the radius and height of a cylinder is r and h. The volume of the cylinder V = πr²h

    Let,

    Radius of cylinder 1 is R and the radius of the cylinder 2 is r.

    The height of the both cylinder is h.

    According to the problem,

    πR²h = 27a and πr²h = 64a

    So,

    πR²h : πr²h = 27a:64a

    or, R²:r² = 27:64

    or, R:r = 3√3 : 8

    Hence,

    The ratio of their bases = 3√3 : 8
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