Question

the volume of a spherical balloon is increasing at a rate of 4 cubic meters per minute. How fast is the surface area increasing when the radius is 3 meters

Answer 1

dv/dt = 4
r = 3, da/dt - ?

Answer 2

a = 4pi*r^2
da/dt = 8pi*r*(dr/dt) = 24pi(dr/dt)

Answer 3

dv/dt = 4pi*r^2(dr/dt)
1 = 9pi(dr/dt)
dr/dt = 1/(9pi)

Answer 4

da/dt = 24pi/(9pi) = 24/9 = 8/3

Answer 5

check for arithmetic errors

Answer 6

hey is there anyway you can rewrite your second response out again i cant figure out how to write it out. thanks