A spherical balloon with a 36cm diameter is being deflated. Its volume V is a function of its radius r according to

Question:

A spherical balloon with a 36 cm diameter is being deflated. Its volume V is a function of its radius r according to

As it's deflating, it is much easier to measure its radius than its volume. Suppose the radius of the balloon is cm at t seconds.

Explanation:

Given

Solving (a):  V'(4)

First, we determine V('r)

Differentiate w.r.t r

Substitute 4 for r and take

This means that the volume of the balloon when the radius is deflated to 4 seconds is 201.143 cm^3

Solving (b): r(4)

Substitute 4 for t in

This means that the radius of the balloon when at 4 seconds of deflation is 11.106 cm

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)