Answer:
The volume is increasing at a rate of 16286 in³/min.
Step-by-step explanation:
a) The volume of a cone is given by:
Where:
r: is the radius
h: is the height
The rate of change of the volume can be calculated by using the chain rule:
Since h = 4/3 r we have:
(1)
With:
= 3 in/min
And by entering the above values into equation (1) we have:
Therefore, the volume is increasing at a rate of 16286 in³/min.
I hope it helps you!