SOLUTION: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of ti

Question 884151: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of time t (in seconds), Recall surface area of a sphere is 4 pi r^2.
I think my time function is 9t but I'm not sure how to do this problem. Please help

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given
(1) A = 4pi*r^2 and
(2) dr/dt = 9
Integrate (2) to get
(3) r = 9t
Now put r of (3) into (1) and get
(4) A = 4pi*(9t)^2 or
(5)
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