Answer:
The rate rate of change of radius is [tex]\frac{1}{48\pi}[/tex] inches per second when the diameter is 12 inches.
The radius is changing more rapidly when the diameter is 12 inches.
Step-by-step explanation:
Consider the provided information.
A spherical balloon is being inflated at a rate of 3 cubic inches per second.
The volume of sphere is [tex]V=\frac{4}{3}\pi r^3[/tex]
Differentiate the above formula with respect to time.
[tex]\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]
Substitute the respective values in the above formula,
[tex]3=4\pi 6^2\frac{dr}{dt}[/tex]
[tex]\frac{1}{48\pi}=\frac{dr}{dt}[/tex]
The rate rate of change of radius is [tex]\frac{1}{48\pi}[/tex] inches per second when the diameter is 12 inches.
When d=16
[tex]3=4\pi 8^2\frac{dr}{dt}[/tex]
[tex]\frac{3}{256\pi}=\frac{dr}{dt}[/tex]
Thus, the radius is changing more rapidly when the diameter is 12 inches.
