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  1. #1
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    composite function involving word problem

    please help, i'm not sure if i'm on the right track.

    A spherical hailstone grows in a cloud. The hailstone maintains a spherical shape while its radius increases at a rate of 0.2 mm/min.

    a) Express the radius, r, in millimeters, of the hailstone, as a function of the time, t, in minutes.

    i came up with the answer,
    r(t) = 0.2t
    but i'm not sure if its right

    b) Express the volume, V, in cubic millimeters, of the hailstone, in terms of r.

    i got,
    V(r) = \frac{4}{3}{\pi}(0.2t)^3

    c) Determine (Vor)(t)

    Vor(t) = \frac{4}{3}{\pi}(0.2t)^3
    not sure if thats right either?

    d) What is the volume of the hailstone 1 h after it begins to form?
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  2. #2
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    Quote Originally Posted by extraordinarymachine View Post
    please help, i'm not sure if i'm on the right track.

    A spherical hailstone grows in a cloud. The hailstone maintains a spherical shape while its radius increases at a rate of 0.2 mm/min.

    a) Express the radius, r, in millimeters, of the hailstone, as a function of the time, t, in minutes.

    i came up with the answer,
    r(t) = 0.2t
    but i'm not sure if its right

    correct

    b) Express the volume, V, in cubic millimeters, of the hailstone, in terms of r.

    i got,
    V(r) = \frac{4}{3}{\pi}(0.2t)^3

    you went one step too fast ...

    \textcolor{red}{V(r) = \frac{4}{3}\pi r^3}

    c) Determine (Vor)(t)

    Vor(t) = \frac{4}{3}{\pi}(0.2t)^3
    not sure if thats right either?

    correct


    d) What is the volume of the hailstone 1 h after it begins to form?

    ... sub in 60 for t and calculate the volume.
    ...
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  3. #3
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    thanks!

    and i did sub in 60 to calculate the volume, and i got 7238? is this correct?
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