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 = 40 centimeters and r = 75 centimeters.

r = 40 cm/min

r = 75 cm/min

(b)

Explain why the rate of change of the radius of the sphere is not constant even though

dV/dt

is constant.

The rate of change of the radius is a linear relationship whose slope is

dV

dt

.

dr

dt

as a function runs parallel to the volume function, which is not linear.

  

The rate of change of the radius is a cubic relationship.

The volume only appears constant; it is actually a rational relationship.

dr

dt

depends on r2, not simply r.

Answer 1

the rading of the Ballon. P-1 u be the volume of the Ballon and she v=Tg3 g=40 When = du rder STX 38 de at e har dr olt. 8=400 v=goo em3/min dr 900 =0.06676 4xт x 40- m/min. When p= 75 e at Фо dr dt 4X TX 752 =0.01273 emmen. The rate of change of the radius is a lisear relationship whose shop is dr dt.