A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 7 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) = 0.)
S(t) = cm^2?

Question

A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 7 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) = 0.) 
S(t) = cm^2?

anonymous · Answer

dr/dt = 7
gives r = 7t+c, c unknown constant
s(r) = 4.pi.r^2 so s(t) = 4.pi.(7t+c)^2
sub in given s(0) = 0, to find c, done.

anonymous · Answer

nope

campbell_st · Answer

so the answer isn't $$SA = 196 \pi t^2$$

anonymous · Answer

yep thats it

campbell_st · Answer

kenny... all you needed to do was some simple algebra... its a worry if you are doing related rates...