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9 September, 03:16

The height of a right cylinder is 4r, where r is the radius. Write a function f in simplest form that represents the ratio of the surface area to the volume.

f (r) =

+2
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  1. 9 September, 03:35
    0
    f (r) = 5/2r

    Step-by-step explanation:

    To find the function f in simplest form that represents the ratio of the surface area to the volume, the relationship between the surface area and volume of a cylinder must first be established.

    The cylinder with radius r and height h has a

    surface area = 2πr (r + h)

    and

    volume = πr²h

    where π is a constant

    hence the ratio of surface area to volume

    = 2πr (r + h) : πr²h

    = 2 (r + h) = rh

    Hence if the height is 6r and the radius is r

    The ratio is

    f (r) = 2 (r + 4r) : r (4r)

    = 10r : 4r²

    = 5:2r
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