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The surface area of a balloon of spherical shape being inflated increases at a constant rate, if initially the radius of balloon is 3 units and after 5 seconds it becomes 7 units, then its radius after 9 seconds is

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Detailed Solution

$S = 4 π γ^{r}, \frac{d s}{d t} = 8 π r \frac{d r}{d t} = K t = 0, r = 3, 36 π = C a t t = 5, r = 7, k_{1} = 32 π 4 π r^{2} = 32 π t + 36 π r^{2} = 8 t + 9 t = 9, r^{2} = 81, r = 9$

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