Answer:
Volume of the pile is increasing at the rate =

Explanation:
Given:
The height of the pile is always twice the radius of the base.
Radius of the conical pile r = 6 inches.
When r = 6
The increasing rate of the radius of pile

We need to find the volume of the pile when the radius of the base is 6 inches.
Solution:
We know the volume of the cone.

Where:
r = radius of the cone
h = Height of the cone
Substitute h = 2r in the above formula because the height of the pile is always twice the radius of the base.


Now, differentiate both side of the equation with respect to t.




Substitute r = 6 and
.



Therefore, volume of the pile is increasing at
in a 6 inches radius of the base.