solving question

Question

A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.

(a)

Find the rates of change of the radius when r = 70 centimeters and r = 85 centimeters.

r = 70			cm/min
r = 85			cm/min

Answer 1

V = 4/3 πr³

dV/dt = 4/3 x 3 πr² dr/dt = 4 πr² dr/dt

dV/dt = 900 [ given] so you can find dr/dt for r = 70, 85 using the above equation

Answer 2

V=(4/3)pi(r^3) take the derivative with respect to time

V'(t) =4pi(r^2)r'

r'(t) = V'/4pir^2

= 900/4pi(75)^2 = 225/pi(75)^2 = 225/pi(5625) = .04/pi = about .04/3.14 = .01327 cm/minute

when r=75

r'=900/4pi(85)^2 = 225/pi(7225) = about 0.03114/pi = .00991 cm per minute

when r=85