+895 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.
+9465 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
+9465 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
