Asked by Anonymous

Sand falls from a conveyor belt at the rate of 20 m^3/min. The sand forms a conical pile where the height of the cone is always 4 times the radius. How fast is the radius changing when the pile is 4 meters high?

Answers

Answered by Reiny
volume of cone
= V = (1/3)π r^2 h, but we know h = 4r or r = h/4
V = (1/3)π (h^2/16)(h)
= (1/48)π h^3

dV = (1/16)π r^2 dr/dt
when h = 4, r = 1
20 = (1/16)π(1) dr/dt
dr/dt = 320/π m/min

check my arithmetic, did it on the screen instead of writing it out first
There are no AI answers yet. The ability to request AI answers is coming soon!

Related Questions