SOLUTION: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 3 cm per second. Express the surface area of the balloon as a function of time

Algebra ->  Functions -> SOLUTION: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 3 cm per second. Express the surface area of the balloon as a function of time      Log On


   

Question 976137: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 3 cm per second. Express the surface area of the balloon as a function of time t (in seconds). If needed you can enter \pi as pi. Recall surface area of a sphere is 4*pi*r^2 .
please give answer (last tutor did not)
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
A=4pi%2Ar%5E2, your surface area formula, variable being r.

dA%2Fdt=4pi%2A2r%2A%28dr%2Fdt%29
dA%2Fdt=8pi%2Ar%28dr%2Fdt%29
Chain Rule is used because radius r is a function of time, and using t for time variable.

Your example specifically specified, dr%2Fdt=3, in cm squared per second.