pleaseee help!!. Calculus!!!...

Question

A large sphere of material is placed in a dissolving liquid.

(a) When the radius is 1 m, it is observed to be changing at 7 cm/hour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time?

 

___ cm³/hr

(b) Suppose, instead, that the liquid is known to dissolve the material at a rate of 1 m³/hour, at what rate will its radius r change with respect to time when r = 1 meter? when r = 1/2 meter?

r = 1			m/hr
r = 1/2			m/hr

(c) What happens to the rate of change of the radius in part (b) as r → 0⁺? r → ∞?

r → 0+
r → ∞

Answer 1

V= 4pir^3/3

V'= (4pi)r'r^2

if r=1, r'=7 then

V'= 4pi(7)(1^2)

V' = 28pi cm^3/hr

if r'=1 m/hr and r= 1 m, then

V'= 4pi m^3/hr

if r'=1 and r= 1/2 m, then

V'=4pi(1)(1/2)^2

V'= pi m^3/hr= about 3.141593 cubic meters per hour

as r approaches 0, V' approaches 0 m^3/hr

as r appoaches infinity, V' approaches infinity m^3/hr