I need help with this problem:
The radius of a spherical balloon is increasing by 2 cm/sec. At what rate is air being blown into the balloon when the radius is 10 cm?
So far what I have is that the volume of the ball is and that the radius where is the time in seconds after the balloon began to inflate. Then the substitution could be made that the volume is . Then to find the rate of change, take the derivative, giving . Then the radius will be 10 cm when t=5 so I plug in 5 for t, giving . This answer feels wrong to me, as the total volume of the balloon is only about 4188.79 cubic cm. Could somebody point out where I went wrong if I have done so, thanks.