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The surface area S (in square meters) of a hot-air balloon is given by S(r)=4(pi)r2, where r is the radius of the balloon (in meters). If the radius is increasing with time t (in seconds) according to the formula r(t)=2/3t3, t≥0, find the surface area of the balloon as a function of the time t.

Oct 9, 2017

#1
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surface area  =  4 * π * (radius)2

And they tell us that the

radius  =  2/3 t3

And we want an equation that gives the surface area for any value of  t  ( that is ≥ 0 ) .

So....instead of calling the radius "radius", we want to say the radius is  2/3 t3  .

surface area  =  4 * π * (2/3 t3)2          Then simplify this equation.

surface area  =  4 * π * 4/9 * t6

surface area  =  16 π t6 / 9             So we can say...

s(t)  =  16 π t6 / 9

Oct 10, 2017

#1
+2

surface area  =  4 * π * (radius)2

And they tell us that the

radius  =  2/3 t3

And we want an equation that gives the surface area for any value of  t  ( that is ≥ 0 ) .

So....instead of calling the radius "radius", we want to say the radius is  2/3 t3  .

surface area  =  4 * π * (2/3 t3)2          Then simplify this equation.

surface area  =  4 * π * 4/9 * t6

surface area  =  16 π t6 / 9             So we can say...

s(t)  =  16 π t6 / 9

hectictar Oct 10, 2017