Question

Air is being pumped into a shperical balloon at the rate of 20 cubic ft. per sec. At what rate is the radius of the balloon increasing at the instant when radius equals 15 ft.?

Answer 1

Nice question. You need to use the formula for the volume of the balloon, as a function of the radius. V(r)=4/3*pi*r^3
Now, you have the rate of volume increase, meaning that V'(r) = 20

Answer 2

oh thanks.

Answer 3

V=4/3 * pi * r^3
V' = 4 pi * r^2 * r'

replace the given then solve for r'

Answer 4

so is the answer 2/(90pi) ft. per sec

Answer 5

yep... looks good but simplify that....

Answer 6

so it would be 1/(45pi)

Answer 7

thanks! :)