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Math Help - Hot-Air Balloon Surface Area

  1. #1
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    Hot-Air Balloon Surface Area

    The surface area S (in square meters) of a hot air balloon is given by:

    S(r) = 4(pi)(r^2), where r is the radius of the balloon (in meters).

    If the radius r is increasing with time t (in seconds) according to the formula
    r(t) = (2/3)(t^3), where t is > or = to 0, find the surface area S of the balloon as a function of the time t.
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  2. #2
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    Quote Originally Posted by symmetry View Post
    The surface area S (in square meters) of a hot air balloon is given by:

    S(r) = 4(pi)(r^2), where r is the radius of the balloon (in meters).

    If the radius r is increasing with time t (in seconds) according to the formula
    r(t) = (2/3)(t^3), where t is > or = to 0, find the surface area S of the balloon as a function of the time t.
    Hello,

    r is a function of t, S is a function of r. Compose both function so that S is a function of t:

    S(r(t))=4 \cdot \pi \cdot \left(\frac{2}{3} \cdot t^3  \right)^2. Expand the bracket:


    S(t)=\frac{16}{9} \cdot \pi \cdot t^6

    EB
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  3. #3
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    ok

    This is exactly what I wanted you to do with the other two questions.

    Thanks!
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