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5 November, 12:52

What are the surface area and volume ratios of a cylinder change if the radius and height are multiplied by 5/4?

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Answers (2)
  1. 5 November, 13:44
    0
    The ratio of the surface areas and volume is 8 ((5y+5x) / 25xy)

    Step-by-step explanation:

    This problem bothers on the mensuration of solid shapes.

    Let us assume that the radius = x

    Radius r=5x/4

    And the height = y

    Height h = 5y/4

    We know that the total surface area of a cylinder is

    A total = 2πrh+2πr²

    We can factor out 2πr

    A total = 2πr (h+r)

    The volume of a cylinder is given as

    v = πr²h

    The surface area and volume ratios

    Can be expressed as

    2πr (h+r) / πr²h = 2 (h+r) / rh

    = (2h+2r) / rh = 2h/rh + 2r/rh

    = 2/r + 2/h

    = 2 (1/r + 1/h)

    Substituting our value of x and y

    For radius and height we have

    = 2 (1/5x/4 + 1/5y/4)

    =2 (4/5x + 4/5y)

    =2*4 (1/5x + 1/5y)

    = 8 (5y+5x/25xy)
  2. 5 November, 15:21
    0
    Ratio of surface area = 25/16

    Ratio of volume = 125/64

    Step-by-step explanation:

    The surface area and volume of a cylinder are given by the formulas:

    Surface area = 2 * (pi*r^2 + pi*r*h)

    Volume = pi*r^2*h

    If we increase the radius and height by 5/4, we have that:

    New surface area = 2 * (pi * (5/4*r) ^2 + pi * (5/4) * r * (5/4) * h) = (5/4) ^2 * 2 * (pi*r^2 + pi*r*h) = (5/4) ^2 * Surface area

    New volume = pi * (5/4*r) ^2 * (5/4) * h = (5/4) ^3 * pi*r^2*h = (5/4) ^3 * Volume

    So the ratios are:

    ratio of surface area = New surface area / Surface area = (5/4) ^2 = 25/16

    ratio of volume = New volume / Volume = (5/4) ^3 = 125/64
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