Chloe is a pharmacist and wants to know the height of a medicine bottle received from a supplier. The supplier informed her that

Question

Chloe is a pharmacist and wants to know the
height of a medicine bottle received from a
supplier. The supplier informed her that the
radius of the medicine bottle is one-fourth its
height. Chloe knows that the medicine bottle
has a volume of V cubic inches.
Which of the following functions would best model the situation above?
O
cube root
O
square root
O
exponential
O
step

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Katherine 3 months 2021-10-24T15:23:40+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-24T15:25:09+00:00

    The given situation would be a best model of cube root.

    Solution:

    Generally, medicine bottles will be cylindrical in shape. Since the shape of the bottle is not given we can assume that the bottle is in cylindrical shape.

    Given information:

    Radius of the bottle (r) = one fourth of its height (h)

    \Rightarrow r=\frac{1}{4}\times h

    Volume of the bottle = V cubic inches

    The formula of the volume of a cylinder is as follows,

    \Rightarrow V=\pi r^{2} h

    This can be re-written as h=\frac{V}{\pi r^{2}} as we do not know the height.

    On plugging-in the given values we get,

    \Rightarrow h=\frac{V}{\pi \times(\frac{h}{4})^{2}}\rightarrow \frac{V}{\pi \times\frac{h^2}{16}}\rightarrow \frac{16V}{\pi\times h^2}

    On solving we get,

    \Rightarrow h\times h^2 = \frac{V}{\pi}

    \Rightarrow h^3 = \frac{V}{\pi}

    On taking the cube root on both sides we get,

    \Rightarrow h=\sqrt[3]{\frac{V}{\pi}}

    Therefore, cube root would be the best model of the given solution.

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