Answer:
The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.
Because the radius is changing more rapidly when the diameter is 12 inches.
Step-by-step explanation:
Let be the radius, the diameter, and the volume of the spherical balloon.
We know and we want to find
The volume of a spherical balloon is given by
Taking the derivative with respect of time of both sides gives
We now substitute the values we know and we solve for :
The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.
When d = 16, r = 8 and is:
The radius is increasing at a rate of approximately 0.025 in/s when the diameter is 16 inches.
Because the radius is changing more rapidly when the diameter is 12 inches.