i pasted it below

Question

sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. how fast is the radius increasing when its 6 feet and the volume is increasing at a rate of 24 cubic feet per minute

Answer 1

Volume V=⅓πr²h where r=radius and h=altitude or height=4r/3.

V=⅓πr²(4r/3)=4πr³/9.

dV/dt=dV/dr.dr/dt=4πr²/3.dr/dt=24 cu ft/min.

When r=6, 48πdr/dt=24, dr/dt=1/(2π)=0.1592ft/min. (1.91 in/min approx).