Amachine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. the height of the pile is always twice the length of the base diameter. after 5 minutes, how fast is the area of the base increasing?

Start with Volume equation for a Cone in terms of base Area.

Next relate height in terms of base Area: (Note base = pi*r^2)

New volume equation is:

Take derivative with respect to time:

Sub in rate for volume, solve for dA/dt

Finally we need the Area after 5 min, given the volume after 5 min is 100.
Go back to Volume equation and solve for sqrt(A)

Final